President Bush pledged Tuesday to reduce the United States' long-range nuclear arsenal by two-thirds or more over the next decade, to between 1,700 and 2,200 warheads. Russian President Vladimir Putin said he would "try to respond in kind."

Emerging from their first White House summit, Bush said his decision would leave the United States with a supply of warheads "fully consistent with American security."

At a joint news conference, the two men said they had found common ground on numerous issues — the war on terrorism and the shape of a future government in Afghanistan among them. But they said disagreements remain over American plans to develop a missile defense shield, adding they would continue discussions on the subject over the next two days in Texas.

In remarks that relegated the Cold War to a distant memory, Bush said the discussions with Putin herald "a new day in the long history of Russian-American relations, a day of progress and a day of hope."

Said Putin: "We intend to dismantle conclusively the vestiges of the Cold War."

Bush greeted Putin at midmorning in the Oval Office, the fourth time the two men have sat down together. They lunched in the mansion's Blue Room and then addressed reporters in the East Room from two brand-new lecterns specially designed for Bush and built by hand by the White House Communications Agency.

Bush's announcement of unilateral cuts redeemed a pledge he made during last year's presidential campaign. The United States currently has roughly 7,000 intercontinental nuclear warheads. Russia has an estimated 5,800.

The president also said he would work to "end the application" of Cold War-era legislation that restricted trade.

The president said he and Putin also had agreed to support a United Nations call for a "broadly based and multiethnic" government in Afghanistan to replace the Taliban.

"Russia and America share the same threat and share the same resolve" to battle terrorism, he said. "We will fight and defeat terrorist networks wherever" they exist.

The two presidents found one more thing to agree on — support for Pakistani President Pervez Musharraf. Bush said the Pakistani leader "deserves our nation's support," and Putin said a few moments later, "We agree with this."

Musharraf has led his country firmly into the coalition against the Taliban rulers in Afghanistan.

Putin made clear he continues to oppose Bush's plan for a missile defense system.

Bush came to office pledging to develop a shield, even if it meant scrapping the 1972 Anti-Ballistic Missile treaty negotiated with the Soviet Union.

In deference to Putin's assistance in the war against terrorism, though, the administration recently announced a delay in some missile defense tests, saying it wanted to avoid bumping up against the treaty's prohibitions.

Bush's comment about trade restrictions referred to the 1974 Jackson-Vanik legislation. Designed to lift emigration curbs on Jews and other minorities, it forced the Soviet Union to permit mass departures in order to qualify for trade privileges.

"Russia is fundamentally a different place," Bush said.

Because of progress on Jewish migration, he said, "my administration will work with Congress to end the application of Jackson-Vanik to Russia."

Bush said he and Putin had spent considerable time discussing the situation in Afghanistan, where the ruling Taliban abandoned the capital city of Kabul overnight.

Bush said the withdrawal signaled that "we're making great progress in our objective, and that is to tighten the net and eventually bring Al Qaeda to justice and at the same time deal with the government that's been harboring them."

Bush made clear he hasn't changed his views on the ABM Treaty, Putin's concerns notwithstanding. "I'm convinced the treaty is outdated and we have to move beyond it," he said.

He added he expects the two sides will continue their discussions on the topic.

He and Putin are scheduled to meet again Wednesday and again Thursday at the president's ranch in Crawford, Texas.

Bush said he had adopted a new approach on arms control, one based on trust that does not require "endless hours of arms control discussions."

"I looked the man in the eye and shook his hand. But if you need to write it down on a piece of paper I'll be glad to do that. We don't need arms control negotiations to reduce our weaponry in a significant way."

Bush said repeatedly that the northern alliance forces in Afghanistan have pledged they would not occupy Kabul, the capital.

Asked whether northern alliance leaders should be treated favorably because of their presence in the city, Bush said, "there is no preferential place at the bargaining table. All people will be treated the same."