The US and Russian presidents have called on Iran and North Korea to stop their suspected nuclear weapons programmes.
The two men spoke of each other as friends
President Bush said the two leaders shared a common goal - "to make sure that Iran doesn't have any nuclear weapon or a nuclear weapons programme".
Russia's President Putin said they wanted to send "a clear but respectful signal to Iran" to increase its co-operation with the International Atomic Energy Agency (IAEA) which oversees nuclear non-proliferation.
Tehran has, meanwhile, announced that an IAEA team is to arrive in Iran on Thursday for further talks on the country's nuclear programme.
At the two-day meeting at Camp David, near Washington, the presidents also discussed the ongoing conflict in Chechnya and described themselves as "allies in the war on terror".
President Bush said "old suspicions were giving way to new understanding and respect".
There was no suggestion that Russia had agreed to American requests to stop helping Iran's nuclear programme.
Russia is building Iran's first nuclear power station, at the southern port of Bushehr - including supplying uranium over a 10-year period from 2005.
The IAEA, urged by Washington, has raised concerns about Iran's nuclear aims and given Tehran until the end of October to dispel fears that it is secretly developing nuclear arms.
Iran has repeatedly been told by the US and European countries to allow snap inspections of its nuclear facilities.
Tehran denies any plans to develop nuclear weapons. and says its programme is aimed at producing energy.
Officials in Tehran said talks with the IAEA would be about clearing up legal and technical questions.
The BBC's Jim Muir, in the Iranian capital, says many prominent hardliners have been arguing that Iran should pull out of the Nuclear Non-Proliferation Treaty altogether, while moderate voices have urged compliance.
But, he says, nobody wants Iran to be seen to be bowing to American pressures.
Presidents Bush and Putin also urged North Korea to abandon its nuclear programme, though with President Putin saying that should be accompanied by security guarantees for Pyongyang.
No commitment on Iraq
President Putin, who admitted "differences over Iraq", said he would wait for the outcome of the debate over a new UN resolution on Iraq before deciding what assistance Russia would offer.
President Bush said he was not disappointed by the lack of support from other countries for the US occupation.
He said: "I recognise that some countries are inhibited from participating because of a lack of a resolution" from the UN to authorise them to send troops.
About 15,000 more US soldiers and reservists have been told to prepare for service in Iraq because of the failure of other countries to contribute soldiers.
President Bush said Russia and the US had a special responsibility for ensuring international stability and were working together to combat terrorism.
"Both of our nations have suffered at the hands of terrorists and both of our governments are taking actions to stop them.
"No cause justifies terror and terrorists must be opposed
wherever they spread chaos and destruction, including Chechnya."
President Bush, who has in the past condemned Russian's crackdown on Chechen rebels, said a lasting solution to the conflict would only come from "an end to terror, respect for human rights and a political settlement that leads to free and fair elections".