Putin said the Russian and U.S. positions are, in his words, "very close." Bush elaborated, saying the two sides share the same goal, even if they differ on the means to that end.
"First, on Iran, we agree that Iran should not have a nuclear weapon," Bush said. "That's important for people to understand. When you share the same goal, it means [that] as you work diplomatically, you're working toward that goal. Secondly, I am confident that the world will see to it that Iran goes to the UN Security Council if it does not live up to its agreements. And when that referral will happen is a matter of diplomacy."
Iran says its nuclear program is solely for peaceful energy production. Russia is helping the process, and the Russian Foreign Ministry says there is no need to refer Tehran to the Security Council for possible sanctions.
That decision is up to the UN's International Atomic Energy Agency (IAEA), which may make a decision on Iran when it meets next week -- or it may postpone the vote.
Washington reportedly prefers a quick decision, and it may get its way. Iran's state-run Islamic Republic News Agency reports that Iranian President Mahmud Ahmadinejad said his country is willing to provide other Islamic states with nuclear technology.
On another nuclear issue, Bush and Putin said their positions on ending North Korea's weapons program are much closer, although the talks in Beijing remain stalled.
Bush said he hopes he can help Russia become a member of the World Trade Organization (WTO) by the end of this year.
Bush and Putin also made much of their personal relationship during the briefing. One reporter commented that this seems to provide much of the substance of the two countries' relationship, and she asked what will happen after the two men leave office.
Putin replied simply that the relationship goes far deeper, to the countries' mutual security and economic interests. And Bush said he and Putin have left a legacy that includes deep strong ties and the Treaty of Moscow, signed nearly four years ago, which reduces the two countries' nuclear arsenals.
In general terms, Bush said, he and Putin will have bequeathed to future leaders what he called a "strategic dialogue."
"There's a kind of strategic dialogue. We get in habits sometimes, and the idea of setting a way for governments to talk to each other at different levels of government is a good legacy," Bush said. "And so we do have three more years -- which I found out is a long period of time -- and we'll be able to do more together that people, that future governments, will view as a way to move forward and to keep the peace and to deal with big issues in a complex world."
Bush also said he hopes he can help Russia become a member of the World Trade Organization (WTO) by the end of this year. Putin said he is grateful to Bush for understanding Russia's interest, but it is unclear whether Bush can succeed in winning Russia's entry into the trade group.
Russia sells its natural gas domestically at a drastically lower price than it sells it on the world market. The WTO sees this as a subsidy for Russian industry that is not permitted under the organization's rules.
Most analysts say there is no way Russia can accede to the WTO unless it raises the price of gas domestically -- and they say Russia cannot afford to do that.