Glasgow-educated Mr Rouhani won a landslide election victory in June promising a policy of engagement with the West and has had regular diplomatic contacts with the US, but they have been limited to negotiations over Tehran's nuclear programme.
"We want to rebuild and improve our relations to European and North American countries on a basis of mutual respect," he wrote in a contribution for the Sueddeutsche Zeitung newspaper yesterday.
"We are striving to avoid new burdens on relations between Iran and the US and also to remove the tensions that we have inherited," said Mr Rouhani, who has promised to reduce Tehran's isolation and to win an easing of sanctions.
Tehran and Washington severed relations after Iran's 1979 Islamic revolution.
The president said Iran cannot forget everything that has affected relations with the US over the last 60 years, but added: "We must now concentrate on the present and orientate ourselves towards the future."
On Sunday, world powers and Iran suspended their technical talks in Geneva on how to implement an agreement on Iran's nuclear programme until after the Christmas holidays following slow progress.