The talks with Russia and the United States will touch on a proposed new UN Security Council resolution to punish Tehran for pursuing nuclear activities despite international appeals for it to halt uranium enrichment.
"We would prefer to accentuate international pressure so that Iran suspends its sensitive activities. We would like as a priority for new sanctions to be adopted within the framework of the Security Council," said foreign ministry spokesman Frederic Desagneaux.
Kouchner will travel to Moscow on Monday for talks and on Wednesday will fly to Washington for meetings with US Secretary of State Condoleezza Rice.
France has recently been leading a drive within the European Union for tougher sanctions on Iran that it has said could be adopted outside of the UN.
President Nicolas Sarkozy's spokesman has said that the government was talking to French investors about possible new sanctions, but did not elaborate.
The six major powers working to resolve the controversy surrounding Iran's nuclear programme will discuss a draft UN sanctions text September 21 in Washington, the US State Department said this week.
The meeting will include the permanent members of the UN Security Council -- the United States, Britain, Russia, China and France -- plus Germany.
The Security Council has already passed two resolutions imposing sanctions on Iran and calling for a halt to sensitive uranium enrichment work, which Washington fears will turn Iran into a nuclear-armed power.
Iran vehemently denies allegations it is seeking an atomic weapon, saying its nuclear drive is aimed at providing electricity for a growing population whose fossil fuels will one day run out.