The move has raised hopes of progress after years of stalemate.
Mr Rowhani used his first news conference since his weekend inauguration to say he would not surrender Iran’s rights but he wanted to allay Western concerns.
Western countries and Israel say they believe Iran is trying to achieve nuclear-weapons capability.
But Iran says it needs atomic power for energy and medical needs.
The last high-level talks in April between Iran and world powers – the United States, Russia, China, Britain, France and Germany – failed to break the deadlock.
But Hassan Rowhani is seen in the West as a relatively moderate leader, and his victory over conservative rivals in June has raised hopes of a breakthrough in negotiations.
Now, he is indicating a desire to change the tone of negotiations.
“I, as president of the Islamic Republic of Iran, announce that the Islamic Republic has the serious determination for solving this issue, the nuclear issue, while maintaining the rights of the Iranian people. And at the same time, we take into consideration that the worries of the other side have to be eliminated.”
President Rowhani says Iran will not abandon its nuclear program, which he says it would uphold on the basis of international law.
But the sanctions imposed on Iran since 2006, after it refused United Nations demands to suspend its enrichment program, are hurting its economy.
Mr Rowhani has criticised the embargoes, which have had a deepening impact since Europe and the United States recently cut oil imports, the country’s main source of income.
He says international calls for tougher sanctions show a lack of understanding.
“Unfortunately, in the US, there is a pressure group which is a war-seeking group, and it is opposed to constructive dialogue, and it seeks to protect the interest of a foreign country, and it takes orders from it in the US.”
Both the United States and Israel have, in the past, refused to rule out military action to prevent Iran from acquiring a nuclear-weapons capability.
And Israel’s Prime Minister Benjamin Netanyahu has dismissed the Iranian leader’s latest signals on resolving the dispute, calling for increased pressure on Iran instead.
“Iran’s president said that pressures do not work. Not true. The only thing that has worked in the last two decades is pressure. And the only thing that will work now is increased pressure. I’ve said that before, and I’ll say it again, because that’s important to understand. You relent on the pressure, they will go all the way. You should sustain the pressure.”
But an Australian-based analyst of Iranian politics says Mr Rowhani should get credit for shifting the debate from the hardline rhetoric of his predecessor, Mahmoud Ahmedinejad.
Dr Shahram Akbarzadeh a professor of Middle East and Central Asian politics at the University of Melbourne, sees encouraging signs.
He says the signals the new president is sending out signify a real willingness for a rapprochement with the West.
“That’s quite a novel approach to negotiations, because, in the past, Iran has gone to negotiation tables to state its position and has not moved an inch. So, he is prepared to look for common ground in negotiations, and he is hoping that that will generate some goodwill at international fora and, ideally, remove the sanctions on Iran. That’s a big ask, and that has raised a lot of expectations in the population who voted for him.”