Story highlights Dick Cheney says Obama should have ordered a strike to destroy the fallen drone

"We've asked for it back. We'll see how the Iranians respond," Obama says

An Iranian military general says Iran won't send back "the spying equipment"

The Pentagon says it lost contact with a drone and has not recovered it

President Barack Obama said Monday that the United States has asked Iran to return a U.S. drone aircraft that Iran claims it recently brought down in Iranian territory.

"We've asked for it back. We'll see how the Iranians respond," Obama said in a news conference, alongside Iraqi Prime Minister Nouri al-Maliki.

A top Iranian military official previously vowed not to return the unmanned American stealth plane that it says it has.

"No nation welcomes other countries' spy drones in its territory, and no one sends back the spying equipment and its information back to the country of origin," said Gen. Hossein Salami, deputy commander of Iran's military, the semi-official Fars news agency reported Sunday.

"It makes no difference where this drone originated and which group or country sent it to invade our airspace," Salami said. "This was an act of invasion and belligerence."

Former U.S. Vice President Dick Cheney on Monday criticized Obama's decisions on the drone, but for an entirely different reason. He said that, after the aircraft went down, the president should have ordered an airstrike over Iran.

JUST WATCHED Cheney accuses Obama of failing to act Replay More Videos ... MUST WATCH Cheney accuses Obama of failing to act 00:43

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"The right response to that would have been to go in immediately after it had gone down and destroy it," the Republican, who served with President George W. Bush, told CNN's Erin Burnett. "You can do that from the air ... and, in effect, make it impossible for them to benefit from having captured that drone."

Instead, "he asked nicely for them to return it, and they aren't going to," Cheney said.

American officials have not confirmed that the drone shown in a video released last Thursday by Iranian media is a U.S. aircraft. But Pentagon spokesman George Little has said that an American drone is missing and had not been recovered.

Two U.S. officials have confirmed to CNN that the missing drone was part of a CIA reconnaissance mission that involved both the intelligence community and military personnel stationed in Afghanistan.

Iran's official Iran Republic News Agency said the country's armed forces had downed the drone near Kashmar, some 225 kilometers (140 miles) from the border with Afghanistan on December 4.

Salami said downing the plane was "very valuable for us" and "a victory for us and a defeat for our enemies," IRNA reported.

He also said Iran had downed other drones earlier but had not announced those instances because they were not as important.

Iranian TV has aired images of what it says is the drone, an apparently intact RQ-170 drone propped on a pedestal and triumphantly displayed.

One U.S. official said the United States can't be certain it's the real stealth drone, because U.S. personnel don't have access to it. But he added there's no reason to think it's a fake. However, a second senior U.S. military official said that a big question is to how the drone could have remained virtually intact given the high altitude it is believed to have crashed from.

The condition of the drone in the video suggests it was not shot down but suffered a system failure, aviation analyst Bill Sweetman said. There are no burn marks from a fire, no holes and no outward damage. Sweetman noticed a dent along the leading edge but doesn't know what that means.

"It's fairly clear here from the pictures that the outer wings have been separated. The question is, did that happen in the accident or (did they take) them off to move the aircraft?" Sweetman asked.

Iran's U.N. ambassador said in a letter last week that the drone flew 250 kilometers (150 miles) into Iranian territory "to the northern region of the city of Tabas."

The letter from Ambasador Mohammad Khazaee to U.N. Secretary-Genera Ban Ki-moon and the heads of the General Assembly and Security Council said the drone "faced prompt and forceful action" by the armed forces.

"My government emphasizes that this blatant and unprovoked air violation by the United States government is tantamount to an act of hostility against the Islamic Republic of Iran in clear contravention of international law, in particular, the basic tenets of the United Nations Charter," Khazaee's letter said.

He called for U.N. condemnation of U.S. "acts of aggression," as well as "clear and effective measures to be taken to put an end to these dangerous and unlawful acts in line with the United Nations' responsibilities to maintain international and regional peace and security."