Bush said Thursday at the White House that Iran's nuclear ambitions will be on the agenda for the US-Russia summit at the Camp David presidential retreat in Maryland, north of Washington.
"It is very important for the world to come together to make very clear to Iran that there will be universal condemnation if they continue with their nuclear weapons program," he said.
Amid mounting Western suspicions of Iran's actions, the United States has been pressing Russia not to sign an accord that would allow Iran's first nuclear power plant -- which is being built by Russia -- to go online.
But Russia's powerful nuclear industry lobby is determined to press ahead with the 800-million-dollar (700-million-euro) construction of Bushehr, in the south of the country, which Iran is aiming to have ready by 2005.
On Iraq, Putin pointedly avoided harsh criticism of the US invasion of the oil-rich Arab country in his speech before the UN General Assembly, although Russia, like France and Germany, fiercely opposed the war.
Putin's address means that the anti-war coalition between France, Germany and Russia is dead, the Moscow press said Friday.
It "has shown that the troika of opponents to the war in Iraq is definitively in ruins," the liberal daily Gazeta wrote.
And White House officials told AFP that Moscow appeared willing to support a Washington-sponsored UN resolution that would share the financial and military burden of the US-led occupation by authorising a multinational peacekeeping force.
"I believe that President Bush believes President Putin is willing to work toward our shared goal and that is to maximize the contributions from the maximum number of countries in the process of helping the Iraqi people to rebuild Iraq," a White House official said.
"And he believes the Russians and President Putin will be committed to that goal."
Russia Foreign Minister Igor Ivanov spelled out for the first time Moscow's stance on the resolution, saying there had to be a clear time frame for the transfer of power to an Iraqi government.
But Putin sidestepped a question on exactly when that should take place as he appeared before students at a New York university.
The French and German leaders have called for a faster handover of power to Iraqis, which Washington says is unrealistic.
Observers in Moscow believe that Russia is in fact negotiating with the Americans to obtain a share of oil contracts for Russian companies in Iraq, which has the world's second-largest reserves.
"The position on Iraq is getting closer. Russian energy interests will be respected if Russia supports the UN resolution," Vyacheslav Nikonov, director of the Fond Politika think-tank in Moscow, predicted.
And while the warmth may have gone out of the friendship between Putin and Bush, who famously said in July 2001 that he had looked into the ex-spy's soul and found he could trust him, there are common interests.
Washington remains extremely keen on boosting Russian oil shipments to diversify its energy supplies away from the volatile Middle East. A US-Russian energy summit took place in Saint Petersburg just before the Camp David talks.
"The spotlight will be on economic relations," a senior US official said of the presidential summit. "They will also discuss military cooperation, like missile defense."
An editorial in The Washington Post Friday accused Putin of handling Muslim-majority Chechnya with a Stalinist policy.
White House spokesman Scott McClellan said "it's important that we -- that terrorism be confronted and stopped everywhere, including in Chechnya.
"But we've always said that any lasting solution to the conflict in Chechnya will require putting an end to terrorism, putting an end to human rights abuses, and punishing those who commit them, and then concluding a political settlement of which free and fair elections will be an important part."