Senior negotiators from both camps met behind closed doors for a second day of talks at Geneva's upscale Hotel President Wilson, which was sealed off to the media.
The meeting is part of a fresh diplomatic drive in the face of a looming July 20 deadline for a final deal between Iran and the P5+1 group of world powers.
"Iran will do its best for a final deal with the P5+1," said Rouhani, a former nuclear negotiator, speaking in Turkey.
"Iran is ready to sit at the negotiating table for a solution" to both the nuclear dispute and "unfair sanctions", he said.
After over three hours of talks today morning, Iran's deputy foreign minister and nuclear pointman Abbas Araqchi said the climate was "positive".
Washington warned of "tough choices" as fellow P5+1 members try to build momentum in the crunch negotiations.
The US-Iran meeting began yesterday with a five-hour session, the first time since the 1979 Islamic Revolution that American and Iranian negotiators have held direct, official nuclear talks.
They have also sat down together within the P5+1 process.
The P5+1 comprises the five permanent UN Security Council members Britain, China, France, Russia and the United States, plus Germany.
They secured an interim deal with Iran in November after marathon talks in Geneva.
The deadline for a final accord was July 20, but several players including Iran have already said a six-month extension may be needed.
Washington and the other P5+1 states are seeking solid commitments that will ensure Iran's stated desire for a peaceful atomic energy programme is not a covert attempt to build a nuclear bomb.
Tomorrow, Iranian negotiators are set to meet in Geneva with their French counterparts, before heading to Rome for talks with Russian officials, then hold a session in Tehran with Germany on Sunday.
