In a joint news conference at the White House on the first day of a three-day summit meeting, Bush said he had informed Putin "that the United States will reduce our operationally deployed strategic nuclear weapons to a level between 1,700 and 2,200 over the next decade."
"Current levels of our nuclear forces do not reflect today's strategic realities," Bush said, and the 1,700 to 2,200 range was a "level fully consistent with American security." These are nuclear missiles deployed on submarines and land silos in the United States and Russia. They are capable of wiping out virtually all the population centers of the two countries.
When codified, this will be one of the largest reductions of nuclear arms in history and the largest since both sides redeployed tactical nuclear weapons in the early 1990s, drawing them back from their frontline services.
A senior White House official said Tuesday the president was determined to reduce U.S. nuclear stockpiles, regardless of Russia, barring developments outside his expectations for the course of strategic need.
Putin was not expected to put specific numbers on Russia's reduction of nuclear weapons until he had returned to Moscow to confer with his advisors on the U.S. number, the official said.
Under Bush's plan, warheads would be removed from missiles but would not be fully dismantled. The physical job of removing the warheads can take time, which is why the 10-year time frame was necessary. Washington was also open to Russia verifying the U.S. reductions, the White House official said.
The Russians have been seeking a reduction of this magnitude for some time. The Russian Federation's nuclear arsenal has degraded over the years and the cost of maintaining it is sapping the nation's resources.
Earlier in the day, Bush took Putin on an unscheduled tour of the White House, including its swimming pool and the South Lawn tree swing where Amy Carter and the Kennedy children once played.
Both men then rejoined their delegations inside the White House, where Bush praised his Russian counterpart, saying, "You're the kind of guy I'd like to have in a foxhole with me."
In their meeting, which lasted about an hour, Putin spoke at length about the importance of completing the mission in Afghanistan.
"Until the al Qaida (network) is brought to justice, we are not leaving. As great nations we are the most vulnerable targets," said Putin, according to a participant.
The two presidents did not report any decisions on the other strategic issue, the 1972 Anti-Ballistic Missile Treaty. Bush said the two countries "have different points of view about the ABM Treaty," but they will continue discussions over the next few days in Crawford, Texas.
A senior White House official said they were not expected to reach an agreement on missile defense.
The United States wants to develop a defense against missiles, which is not permitted under the 1972 ABM treaty. Bush has said that the treaty is outmoded and that the real danger is not from a nuclear attack by either country on the other, but from smaller states that have one or two missiles.
Putin at first opposed Bush's plan, claiming the treaty was the framework of nuclear peace for nearly 30 years.
But as the relationship between the two leaders warmed over the past months, particularly after the Sept. 11 terrorist attacks against the United States, U.S. officials said the Russian position was softening. Two weeks ago in Moscow, Putin said Russia was "flexible" on the issue.
"On the issue of missile defense," Putin said Tuesday, "the position of Russia remains unchanged."
The summit moves Wednesday to Bush's ranch in Crawford, Texas, where both leaders are expected to continue talking about missile defense.
Arms control experts believe that Putin ultimately will agree to let the United States conduct tests without triggering the ABM treaty's sanctions -- in effect, as one arms control expert said by "turning a blind eye."
Bush said he is convinced the treaty "is a piece that's codified a relationship that no longer exists. It codified a hateful relationship. And now we have got a friendly relationship."
Bush also said he will move to lift the terms of Jackson-Vanik, a Cold War law that required countries of the old Soviet Union to meet certain human rights standards before they could trade with the United States The law covers several of the U.S. allies in the war on terrorism, Uzbekistan among them.
Another difficult issue between the two countries is arms sales to Iran, which was raised when the two leaders had lunch Tuesday at the White House. Russia's desire to enter the World Trade Organization was also expected to be on the agenda for Wednesday.
White House officials said the U.S. summit had met expectations and that relations with Russian had advanced further than anticipated when Bush took office.