AL ASAD AIR BASE, Iraq – America may be able to reduce its troop levels in Iraq after the January elections if security improves and Iraqi government forces continue to expand and improve, Defense Secretary Rumsfeld said yesterday.

In a question-and-answer session with hundreds of Marines assembled in a concrete-lined aircraft hangar at this desert air base in western Iraq, Mr. Rumsfeld was asked what the future holds for the length and frequency of troop deployments in the country.

Mr. Rumsfeld, on his first visit to Iraq since its interim government was installed in June, said the insurgent violence is likely to get worse in the weeks ahead, so troop reductions are almost out of the question. America now has about 135,000 troops in Iraq.

“Our hope is that as we build up Iraqi forces, we will be able to relieve the stress on our forces and see a reduction in coalition forces over some period of time, probably post-Iraqi elections,” the Pentagon chief said. “But again, it will depend entirely on the security situation here in this country.”

Later, Mr. Rumsfeld flew to the northern city Kirkuk, where he received a briefing from the top commander in that area, Major General John Batiste, and other American officers, who told him insurgent attacks had decreased in number since July. They also said American-trained Iraqi forces in the Kirkuk area were improving so quickly that they recently were able to plan and execute offensive operations on their own, with American officers present only as observers.

Mr. Rumsfeld had dinner with South Korean soldiers, members of the Zaytun Division, who began arriving in Iraq last month to provide combat and support troops in the area around the city of Irbil, west of Kirkuk.

Before Mr. Rumsfeld appeared at the main operating base of the 3rd Marine Air Wing, the approximately 1,500 Marines in his audience were given instructions by Sergeant Major Dennis Reed on what not to ask. “Don’t ask when you’re going home. We’ll tell you when you’re going home,” Sergeant Reed said.

Mr. Rumsfeld then gave a pep talk and fielded questions at a town hall style meeting. “We’re so fortunate to be able to count on you in this time of peril,” Mr. Rumsfeld said, to applause.

The secretary then flew to Baghdad, where he met with the American ambassador, John Negroponte; the top American commander in Iraq, General George Casey; and the American officer in charge of training and equipping Iraqi security forces, Lieutenant General David Petraeus. Accompanying Mr. Rumsfeld on the flight in a Black Hawk helicopter was Iraq’s interim defense minister, Hazem Shaalan.

As a reminder of the shaky security situation in the Iraq capital, the fleet of Black Hawks carrying Mr. Rumsfeld and his entourage flew at high speed, just above rooftop level, occasionally zigzagging en route to the International Zone, where the American Embassy is located.

In a brief exchange with reporters after the Baghdad meeting, Mr. Rumsfeld grew agitated by questions about the possibility of needing to bring in extra American troops before Iraq’s scheduled elections.

“There’s a fixation on that subject!” he said with exasperation. “It’s fascinating how everyone is locked on that.”

He asserted that the press and others are ignoring the facts that the number of American-trained Iraqi security forces is growing – standing now at roughly 100,000 – and that they are fighting and dying.

“They do exist. Over 700 of them have been killed,” Mr. Rumsfeld said.

General Casey told reporters that he and Mr. Rumsfeld did not discuss American troops levels in their meeting.

“If I need more troops, as the secretary said, I will ask for them,” the general said. He added that the number of trained Iraqi forces will increase by 45,000 by election time.

Mr. Rumsfeld also met with Prime Minister Allawi, at the government’s headquarters not far from the American Embassy. The two sat side-by-side in large chairs, an Iraqi flag behind them.

Mr. Allawi, referring twice to Mr. Rumsfeld as the secretary of state, thanked him for America’s help in giving Iraqis their freedom. Mr. Rumsfeld replied that it was important for him to meet with Iraqi leaders to talk about preparations for elections and “to make sure they happen and this country continues on a path toward democracy.”

The trip was Mr. Rumsfeld’s sixth to Iraq but his first to Anbar province, which includes portions of the Sunni Triangle north and west of Baghdad. The region had been the heart of tribal support for Saddam Hussein.

Anbar is an insurgent stronghold, including the provincial capital of Ramadi, and the city of Fallujah, where Marines fought fierce battles in the spring. In recent months, Marines have taken a large proportion of American casualties. In light of the violence in Iraq, Mr. Rumsfeld’s visit was not announced in advance. Reporters traveling with the secretary were instructed not to disclose his plans until he arrived in Iraq from Bahrain aboard an Air Force C-17 cargo plane.

Later this week, Mr. Rumsfeld is attending a meeting of NATO defense ministers in Romania. Expected to be on the agenda Wednesday and Thursday are issues such as the alliance’s role in Afghanistan, where it commands the International Security Assistance Force, and Iraq, where it has agreed to help train Iraqi security forces.

Another expected topic is the work under way to terminate the NATO peacekeeping mission in Bosnia by the end of this year, when it is to be converted to a European Union security mission. America now has about 700 troops in Bosnia and 1,800 in Kosovo.

On Saturday, Mr. Rumsfeld was aboard an American aircraft carrier in the Persian Gulf for a meeting with 18 of his counterparts from American allies in the terrorism fight.