Top administration officials and lawmakers have left the White House after a classified briefing lasting over an hour, about Iran's sudden downing of an American surveillance drone in the Middle East -- and a "measured" U.S. response, they suggested, is likely coming soon.

Amid mounting tension between the U.S. and Iran, the White House earlier Thursday invited House and Senate leaders and Democrats and Republicans on the House and Senate Intelligence and Armed Services Committees to meet with President Trump in the White House's secure Situation Room.

Others who arrived for the meeting included CIA Director Gina Haspel, Chairman of the Joint Chiefs of Staff Gen. Joseph Dunford, Secretary of State Mike Pompeo, acting Defense Secretary Patrick Shanahan and Army Secretary Mark Esper, whom Trump has said he'll nominate as defense secretary.

Shanahan was spotted outside the White House carrying a folder stamped "SECRET/NOFORN," an intelligence classification category prohibiting distribution to anyone outside the government.

Senate Majority Leader Mitch McConnell, R-Ky., told Fox News that "we had a good briefing" and that the Trump administration would engage in "measured responses."

Outgoing Acting Defense Secretary Patrick Shanahan carrying a document labeled secret as he arrived for a meeting with President Trump about Iran at the White House on Thursday. (AP Photo/Alex Brandon)

McConnell confirmed the U.S.'s firm position that the drone was operating in international airspace, even as Iran has tried to make the case that the drone had "violated" Iranian airspace.

In a statement, House Republican Leader Kevin McCarthy and Ranking Members Michael McCaul of Texas (House Foreign Affairs), Devin Nunes of California (House Intelligence), and Mac Thornberry of Texas (House Armed Services) all condemned Iran's "direct attack," and demanded "measured" retaliation.

"Iran directly attacked a United States asset over international waters," the Republicans wrote. "This provocation comes a week after they attacked and destroyed two commercial tankers in international waters. There must be a measured response to these actions. President Trump and his national security team remain clear-eyed on the situation and what must be done in response to increased Iranian aggression. In Congress, we stand ready to support our men and women in uniform, our country, and our allies in the region.”

House Speaker Nancy Pelosi, D-Calif., issued a separate statement after the briefing calling for calm.

TRUMP SAYS IRAN’S US DRONE SHOOT-DOWN MAY HAVE BEEN ‘MISTAKE,’ BUT ‘COUNTRY WILL NOT STAND FOR IT’

“In light of the targeting of an unmanned U.S. drone by Iran, it is essential that we remain fully engaged with our allies, recognize that we are not dealing with a responsible adversary and do everything in our power to de-escalate.

“This is a dangerous, high-tension situation that requires a strong, smart and strategic, not reckless, approach," Pelosi said.

Speaking to reporters, Pelosi said she also was convinced that U.S. intelligence was correct in its assessment that the drone was in international airspace when it was shot down. But, Pelosi added, the Trump administration legally would need to obtain Congress' approval before taking military action.

"We make it very clear that to get involved in any military activities, we must have a new Authorization for Use of Military Force (AUMF)," Pelosi cautioned.

Senate Minority Leader Chuck Schumer, D-N.Y., said he told the president during the briefing that there should be a "robust, open debate," and that Congress should "have a real say."

He said he was worried the administration "may bumble into a war."

"We have an amendment supported by every Democrat to the NDAA in the Senate, led by Senator Udall, which would require Congressional approval of any funding for a conflict in Iran," Schumer said in a statement. "It's supported by all Democrats in the Senate. We are asking leader McConnell to do the right thing and give us a vote next week on the NDAA on that amendment."

Footage on social media also showed Schumer appearing to celebrate after the briefing, but Schumer later clarified that he was happy his mother had been released from the hospital.

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Hours earlier, the Pentagon released video showing the smoke trail of a Navy drone that was shot out of the sky over the Strait of Hormuz by Iran, in what military officials described as an "unprovoked attack."

Trump told reporters that Iran made a "very big mistake" but also said he had the feeling that it might have been the result of someone being "loose" or doing something "stupid," rather than a deliberate provocation by Iran.

The U.S. Navy RQ-4A Global Hawk, an unmanned aircraft with a wingspan larger than that of a Boeing 737, was downed by an Iranian Islamic Revolutionary Guard Corps surface-to-air missile that was fired from near Goruk on Wednesday night, according to Lt. Gen. Joseph Guastella, head of U.S. Air Forces Central Command.

The location where the U.S. drone was down down by a surface-to-air missile fired by Iran. (Department of Defense)

"This was an unprovoked attack on a U.S. surveillance asset that had not violated Iranian airspace at any time during its mission," Guastella said. "This attack is an attempt to disrupt our ability to monitor the area following recent threats to international shipping and free flow of commerce."

Guastella said at the time it was struck by the missile, the drone was operating at a "high altitude" over 20 miles from the nearest point of land on the Iranian coast.

Some Democrats, for their part, blamed Trump for the episode. Presidential candidate Joe Biden said Trump has made military conflict with Iran more likely, and that "another war in the Middle East is the last thing we need."

"Iran directly attacked a United States asset over international waters."
— House Republican Leader Kevin McCarthy, and Ranking GOP Members

Biden said Trump's strategy in Iran has been "a self-inflicted disaster" since the president withdrew the U.S. from the Iran nuclear agreement negotiated when Biden served under then-President Barack Obama as vice president.

The Trump administration called that deal a reckless giveaway to a dangerous regime that only emboldened and empowered its imperialistic and terroristic ambitions. By reimposing sanctions that had been lifted under the Obama-era deal, Trump administration policies largely have crippled Iran's economy, sending inflation above 30 percent and devastating oil revenues.

Biden asserted there's no question Iran "continues to be a bad actor that abuses human rights and supports terrorist activities." But, he added that the U.S. needed presidential leadership.

US NAVY DRONE SHOT DOWN BY IRANIAN MISSILE OVER STRAIT OF HORMUZ IN 'UNPROVOKED ATTACK,' CENTRAL COMMAND SAYS

In a video released Thursday afternoon, the smoke trail of the drone could be seen in a black-and-white video as the craft plummeted.

The Navy RQ-4A Global Hawk drone that was shot down by Iran. (Fox News)

Guastella said the drone landed in "international waters" about 20 miles from Iran. U.S. officials told Fox News that investigators were racing to find the wreckage ahead of Iranian forces.

The U.S. Navy’s RQ-4A Global Hawk drone provides real-time intelligence, surveillance and reconnaissance missions "over vast ocean and coastal regions," according to the military. The drone was deployed to the Middle East in the past few days as part of reinforcements approved by Trump last month.

The high-altitude drone can fly up to 60,000 feet or 11 miles in altitude and stay aloft for 30 hours at a time. It's used to spy on Iranian military communications and track shipping in the busy waterways. Each drone costs up to $180 million.

Also Thursday afternoon, presidential candidate Kirsten Gillibrand, D-N.Y., demanded that Trump abstain from sending American troops into a conflict with Iran without congressional approval.

Members of the 7th Reconnaissance Squadron preparing to launch an RQ-4 Global Hawk at Naval Air Station Sigonella, Italy, in October 2018. (Staff Sgt. Ramon A. Adelan/U.S. Air Force via AP, File)

In recent weeks, the U.S. has sped an aircraft carrier to the Mideast and approved sending 1,000 additional troops "to address air, naval, and ground-based threats" in the region. Mysterious attacks have targeted oil tankers as Iranian-allied Houthi rebels launched bomb-laden drones into Saudi Arabia.

The New York senator outlined her position in a sharply worded letter to the White House on Thursday.

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Gillibrand wrote she was "deeply concerned that your administration's stepped up military presence in the Middle East, in conjunction with your dangerous and confusing rhetoric, may lead the United States into a protracted, costly, and unnecessary war with Iran. Such a war is not authorized, would unnecessarily risk the lives of Americans and our allies, cause enormous human suffering, and destabilize the economy."

Fox News' Travis Fedschun, Hillary Vaughn and The Associated Press contributed to this report.