The Iranian military’s statement said the plane “took the flying posture and altitude of an enemy target” as it came close to an Islamic Revolutionary Guards Corps base. It said that “under these circumstances, because of human error,” the plane “came under fire.”

The military said it would undertake “major reform in operations of all armed forces” to make sure that such an error never happened again. It said Revolutionary Guards officials had been ordered to appear on state media and give the public a full explanation.

In a statement of his own, Iran’s foreign minister, Mohammad Javad Zarif, tried to place some of the blame on the United States, saying on Twitter that the disaster was “caused by U.S. adventurism.” The military’s statement said there had been information suggesting the United States was “preparing to aerially target sensitive defense and key sites and multiple targets in our country, and this led to even more sensitive defense posture by our antiaircraft units.”

The State Department had no immediate comment late Friday about Iran’s admission of responsibility.

Suspicions that an Iranian missile had brought down the plane were raised immediately after the crash Wednesday morning — just hours after Iran fired missiles at two bases in Iraq housing American forces.

The Iranians asked the National Transportation Safety Board to help with the investigation, and the State Department granted waivers to allow the American agency to help. A senior administration official said Friday that he thought the Iranians wanted American investigators there to keep up the appearance that they did not know what had caused the crash.

The official, who spoke on the condition of anonymity because he was not authorized to discuss these matters publicly, said the Iranian military had poor command and control, and that this was reflected in what had happened with the airplane. Communications among officials and between units are often lacking, he said, and confusion can be the norm. Western analysts often overestimate the capability of parts of the Iranian military, he said.

State television in Iran aired footage that it said showed two flight recorder units recovered from the crash site. Processing their data could take more than a month, and the investigation could take up to two years, Hassan Rezaeifar, the head of the Iranian investigation team, said Friday.

“We will continue working with our partners around the world to ensure a complete and thorough investigation, and the Canadian government expects full cooperation from Iranian authorities.”

The 176 people who died on the flight included 57 Canadians, many of them students or faculty at the University of Alberta in Edmonton. About 27 residents of Edmonton were on the plane.

In Canada, Iranians are comparative newcomers: Most arrived after the 1979 Islamic Revolution. Today, by some counts, Canada has the third-largest number of expatriate Iranians in the world and its universities are a top destination for Iranian graduate students.

Canada broke off diplomatic relations with Iran in 2012, but Mr. Trudeau said on Wednesday that Canada’s foreign minister, Francois-Philippe Champagne, would contact his Iranian counterpart, Mohammad Javad Zarif, to underline the need for a proper inquiry.

All sides should ‘learn lessons,’ a Russian official said.

Konstantin Kosachev, the head of the foreign relations committee in the Russian Senate, said Iran’s admission showed the downing of the plane had been a “tragic incident” and should not lead to further escalation between Iran and the West.

“It was a tragic incident; people cannot be returned,” Mr. Kosachev told the Interfax news agency. “The admission of error, although not immediately, and expression of condolences is sufficient to be accepted. With this, the incident should be closed.”

All sides should “learn lessons” from what happened, he said. The disaster “became possible in conditions of real danger of repeat American strikes, this time on Iranian territory, though this in no way justifies the mistake.”

His response to the speaker’s news on Friday was terse. “About time,” he told reporters.

Mr. McConnell has yet to make public his proposed rules for the trial, but he said they would be modeled on a resolution guiding the 1999 trial of President Bill Clinton.

To Democrats’ dismay, that model puts off any decisions on calling witnesses or new evidence until the middle of the trial, after senators are sworn in, the House and White House present opening arguments and senators have a chance to ask written questions. Nor does it guarantee that new evidence will be included.

The minority leader, Senator Chuck Schumer of New York, said Friday that Democrats “would do everything we can to see that the truth comes out.”

Democrats are closely watching a small group of moderate Republicans who are open to calling witnesses, hoping to court their support. With the chamber divided 53 to 47, they need four Republicans to cross party lines if they want a shot at hearing from officials like John R. Bolton, Mr. Trump’s former national security adviser, who are said to have pertinent information about the president’s actions toward Ukraine but evaded House investigators.

Complicating matters, Mr. Trump told Fox News on Friday that he would probably invoke executive privilege to try to shield Mr. Bolton’s testimony if the Senate summoned him. Mr. Trump said he had no problem with what Mr. Bolton might say, but that “for the sake of the office” of the president, he did not want to set a standard of letting a top adviser speak about their interactions.

Mr. Bolton indicated in a statement this week that he would testify if subpoenaed, setting up a potential legal clash.

Even if the trial were to begin Wednesday, it could take several days to be fully organized. Officials in both chambers suggested on Friday that the heat of the trial — beginning with up to 24 hours or oral arguments per side — could begin shortly after the Martin Luther King’s Birthday on Jan. 20. If a majority of senators do vote to call witnesses, that could extend the proceeding by several weeks.

“There was nothing to indicate the flight was in danger,” he said.

American officials have a high level of confidence that a Russian-made Iranian air defense system had fired two surface-to-air missiles at the plane minutes after it took off for Kyiv, one United States official has said. The jet had crashed hours after Iran fired ballistic missiles at American targets in Iraq in retaliation for the killing of Maj. Gen. Qassim Suleimani, the leader of a powerful branch of the Islamic Revolutionary Guards Corps, and was bracing for a possible American response.

But Iran’s failure to close its airspace and ground commercial planes was a key error, according to an American official. Some officials believe Iran may have left its airspace open to avoid telegraphing the precise timing of the airstrike, the official said.

Ali Abedzadeh, the chief of Iran’s Civil Aviation Organization, urged caution at a Friday news conference, saying that investigators could not determine anything about the cause of the crash until they analyzed data from the so-called black-box flight recorders. No missile hit the plane, he said, and it was likely on fire before it crashed.

But the Iranian air defense system used Wednesday is designed to explode near aircraft, creating shrapnel that takes a plane out of the sky, rather than directly hitting it. And footage verified by The New York Times appears to show a missile fired from Iranian territory exploding near where the jet crashed.

State television in Iran aired footage that it said showed two black boxes recovered from the crash site. Processing their data could take more than a month, and the investigation could take up to two years, Hassan Rezaeifar, the head of the Iranian investigation team, said during the news conference.

Normally, Iran has the capacity to download black-box data, but Mr. Rezaeifar said that the devices were damaged, making it difficult to extract information.

“We need special software and hardware which are available in our country, but if we fail to extract the data due to the damages of the black box, we will get help from other countries,” he said, noting that Ukraine, France, Canada and Russia have all expressed willingness to help.