Progress has been made in negotiations with Russia toward an agreement on nuclear arms reductions, Defense Secretary Donald Rumsfeld said Monday.

Wrapping up a five-nation tour, Rumsfeld met briefly with Russian Defense Minister Sergei Ivanov at Moscow's airport, after which both men announced that they had renewed hope that Presdient Bush and Russian President Putin could sign a new arms reduction deal during a summit scheduled in Moscow and St. Petersburg in a few weeks.

The deal, which has been in the works since Putin visited Bush at the president's ranch in Crawford last year, would reduce strategic nuclear arsenals over the next decade from the current levels of more than 6,000 each to around 1,700-2,200 each, a two-thirds drop. 

"It is up to the presidents to make a decision," Rumsfeld said, adding that talks will continue in Washington later this week between Secretary of State Colin Powell and Russian Foreign Minister Igor Ivanov.

The talks hit a snag after Moscow objected to the United States' decision to store the weapons rather than destroy them. 

A senior U.S. defense official traveling with Rumsfeld said Washington would not give up its plan to store some warheads as a hedge against unexpected shifts in the international security picture.

"It's a fact of life" that the Russians must accept, the official said, speaking on condition of anonymity.

The stop in Moscow comes after Rumsfeld spent Saturday in Afghanistan meeting with Afghan interim leader Hamid Karzai, other Afghan leaders and U.S. troops stationed there.

Asked about progress on the war against terror in Afghanistan, Rumsfeld expressed confidence that the Taliban have been denied locations to assemble, but added: "The reality is there's a lot of work yet to do and there will be more violence between now and the time it's over."

Rumsfeld also visited Kyrgyzstan, Turkmenistan and Kazakhstan during his trip, where he received assurances on continued support for the war against terror, including the use of a military base in Kazakhstan for coalition planes and the continued delivery of humanitarian support from Turkmenistan.

The Associated Press contributed to this report.