"It will be on the agenda of my discussions with Mr Putin," Bush told reporters at the White House on Thursday.
Bush said he had discussed Iran with several leaders while at the UN General Assembly in New York on Tuesday and Wednesday.
"The response was very positive, and people understand the danger of Iranians having a nuclear weapon program," Bush said.
"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."
International Atomic Energy Agency inspectors found new traces of enriched uranium in Iran but do not know if it was made in Iran or contamination from imported equipment, diplomats said Thursday.
At stake is whether Iran is producing highly enriched uranium for nuclear weapons, as the United States claims, or whether the traces came along with second-hand equipment bought abroad, as Tehran says.
The traces were found in August at the Kalaye Electric Company near Tehran, said the diplomats in Vienna, where the IAEA is based.