BAGHDAD — Vice President Cheney, marking five years since the American invasion of Iraq, warned today against large drawdowns of American troops that could jeopardize recent security gains.

At a news conference with American Ambassador Ryan Crocker and General David Petraeus, the top commander in Iraq, Mr. Cheney said that given the nearly 4,000 American troop deaths and billions of dollars spent on the war, it is very important that “we not quit before the job is done.”

Mr. Cheney credited reductions in violence to President Bush’s decision to deploy an additional 30,000 troops to the war zone. In deciding whether to draw back more than the 30,000 before he leaves office, Mr. Cheney said President Bush will weigh whether America can continue on a track toward political reconciliation and stability in Iraq.

“It would be a mistake now to be so eager to draw down the force that we risk putting the outcome in jeopardy,” said Mr. Cheney, on an unannounced visit to Iraq. “And I don’t think we’ll do that.”

Asked whether the progress that’s been made on the security front is an indication of more troop withdrawals after July, Mr. Cheney answered “No it does not.”

General Petraeus and Mr. Crocker are working on a status report on the war and will testify to Congress next month. General Petraeus said discussions on the report would continue within the chain of command this week and then with the president.

“We’re keenly aware of the strain and the stress that these extended deployments have put on soldiers and their families and we would love to draw down further, but that is dependent on conditions on the ground,” he said.

At the news conference, a rarity for the vice president, Mr. Cheney was asked questions ranging from Iran to oil to the upcoming presidential election.

The vice president brushed off Iranian President Ahmadinejad’s recent visit to Baghdad and said it was not widely discussed at his meetings with Iraqi leaders. “We obviously noted Ahmadinejad’s visit to Iraq,” Mr. Cheney said, adding that he did not find it surprising that the leader of a neighboring nation would visit.

Mr. Cheney said American allies in the Arab world should send ambassadors to Iraq as a counter to Iran, which is seeking a greater sphere of influence in the Middle East and is accused of supporting terrorists and extremists in Iraq.

“A number of them have indicated that they’re prepared to do it, but have not yet done it,” Mr. Cheney said.

In a country with the world’s third-largest known crude oil reserves, Mr. Cheney acknowledged that the declining value of the American dollar was a factor in helping drive up global oil prices. He said another problem was that there was not a lot of excess capacity.

Mr. Cheney steered clear of sharing any concerns that his Iraqi hosts have about the upcoming presidential election. “I’m not here to sell a particular partisan view to our hosts,” he said just hours after the Republican Party’s expected nominee, Senator McCain, left Baghdad after a weekend visit.

Asked whether he came on his third vice presidential visit to Iraq with a weaker hand because he and Mr. Bush have just 10 months left in office, Mr. Cheney said: “I don’t feel any sense of the loss of influence, if you will. If anything, the successes that we’ve demonstrated here have given us greater credibility than would have been the case if we hadn’t had the surge and the progress of the last 12, 15 months.”

Mr. Bush’s decision last January to increase troops put to rest any notion that either “here inside Iraq or in the region that people could ‘wait us out,'” Mr. Cheney said.

Mr. Cheney landed at Baghdad International Airport, then flew by helicopter into the dusty, heavily secured Green Zone for talks with American military and diplomatic officials and the Iraqi prime minister. It was Mr. Cheney’s third vice presidential trip to Iraq where 160,000 American troops are deployed and the American death toll is nearing 4,000. Mr. Cheney was expected to make stops throughout the country.

Mr. Cheney’s motorcade zigzagged through Baghdad to meetings as helicopter gunships circled overhead. Explosions were heard in parts of the city, but none were near the vice president.

“It’s good to be back in Iraq,” Mr. Cheney said after an hour-long meeting with Prime Minister al-Maliki of Iraq.

Mr. Cheney, who was in Iraq 10 months ago, said the Iraqis have made legislative advances that would be vital to the country’s future. He also said there was no question but there had been a dramatic improvement in security.

Mr. al-Maliki, speaking through an interpreter, also cited security improvements and said he and the vice president had talked about negotiations under way to spell out the legal basis for the presence of American troops on Iraqi territory and to establish the legal rights and obligations of the troops, the so-called “status of forces agreement.”

“There is still a lot of difficult work that must be done,” Mr. Cheney said after sitting down with the leader of the Supreme Islamic Iraqi Council and one of the most powerful politicians in the country, Abdul-Aziz al-Hakim.

“But as we move forward, the Iraqi people should know that they will have the unwavering support of President Bush and the United States in consolidating their democracy,” Mr. Cheney said.

Oman was scheduled to be the first stop on Mr. Cheney’s 10-day trip to the Mideast, but last night, he left Air Force Two parked on a tarmac in England and boarded a C-17 for the final five and a half hours of the 13-hour flight to the Iraqi capital.

The future of Iraq will be discussed in his closed-door talks with leaders of Oman, Saudi Arabia, Israel, the Palestinians, and Turkey.