The joint warning came after a summit on Saturday between US President George Bush and Russian President Vladimir Putin that was marked by signs of an increasingly strong relationship, despite differences over Iraq.
The Russian leader refused to pledge his country's help to the US occupiers in Iraq until a new UN resolution is passed.
The two-day summit at the Camp David presidential retreat concentrated on the nuclear programmes in Iran and North Korea - the two remaining members of Bush's so-called "axis of evil" after the fall of Saddam Hussein's Iraq regime - and US attempts to secure international help in Iraq.
Putin, whose country is helping Iran to build a nuclear reactor, told a joint press conference that a "clear but respectful signal" should be sent to Tehran about the need to cooperate with the International Atomic Energy Agency (IAEA) over its nuclear facilities.
Putin went on that "Russia has no desire and no plans to contribute in any way to the creation of weapons of mass
destruction, either in Iran or any other spot or region in the world."
The United States has accused Iran of seeking nuclear weapons and is pressing Russia not to complete an accord that would allow Iran's first nuclear power plant to go online in 2005.
"Russia believes that ensuring nuclear non-proliferation should be accompanied by extending to North Korea guarantees in the security sphere"
The IAEA has set an 31 October deadline for Iran to account for its nuclear activities. But the agency has postponed sending a monitoring mission that was to leave on Sunday to give Iran more time to prepare.
Russia is meanwhile stalling on an accord to provide uranium fuel for the new reactor.
Bush, who has proposed the development and use of "small-yield" nuclear weapons, said Russia and the United States "share a common goal, and that is to make sure Iran doesn't have a nuclear weapon, or a nuclear weapons programme."
"We also understand that we need to work together to convince Iran to abandon any ambition she may have," Bush added.
Turning to North Korea, which the United States says already has nuclear weapons, Putin said a "favourable atmosphere for a constructive dialogue" must be built up to entice Pyongyang to end its weapons drive.
Putin said a "priority" must now be made of trying to defuse the heightened tensions on the Korean peninsula caused by the new nuclear crisis and creating "a favourable atmosphere for a constructive dialogue."
Putin and Bush found some common ground
He said "Russia believes that ensuring nuclear non-proliferation should be accompanied by extending to North Korea guarantees in the security sphere. We intend to continue our joint work with the United States in resolving this issue."
Russia and the United States were among the five nations that held talks with North Korea in Beijing last month on its nuclear programme.
Waiting on UN
Putin said Russia's contribution to policing and rebuilding Iraq could only be decided after a new UN resolution was passed, which set out a United Nations role in the war-stricken country now run by a US-led coalition.
The Russian leader insisted his country wanted to see Iraq normalised "as soon as possible."
He added, "At the same time, we understand it is a complicated process that should be based on a solid legal and administrative basis and should go ahead stage by stage."
"The degree and extent and level of Russia's participation in the restoration of Iraq will be determined when we know the parameters of the new resolution on Iraq," Putin told the press conference.
But Bush insisted he was still "pleased" with the level of international help he was getting in Iraq.
"I like (Putin). He's a good fellow to spend quality time with"
"I recognize that some countries are inhibited from participation because of the lack of a UN resolution. We are working to get a satisfactory resolution out of the United Nations. We spent some time talking about that today."
Bush highlighted the high degree of "trust" he had built with the Russian leader despite differences that they had, particularly over Iraq.
The US leader was careful to call for an end to hostilities and "terrorist" attacks in Chechnya.
"Terrorists must be opposed wherever they spread chaos and destruction, including Chechnya," Bush said, with Putin at his side.
"Vladimir and I had very frank discussions about Iraq. I understood his position. He understood mine, but because we've got a trustworthy relationship, we're able to move beyond any disagreement over a single issue. Plus, I like him. He's a good fellow to spend quality time with," the US leader declared.