"We are the people of interaction and talks, with seriousness and without wasting time, if the other sides are ready," he said at his first news conference since assuming office on Saturday.
"Iran's peaceful nuclear programme is a national issue... we will not give up the rights of the Iranian people," he said.
"We will preserve our rights based on the international regulations," he added, in reference to Iran's insistence that it has the right to peaceful use of nuclear power as a signatory to the Non-Proliferation Treaty.
Rouhani hit out a call by 76 US senators for tougher sanctions from Washington even as he took office with a call for constructive engagement.
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He said Friday's letter from the US lawmakers to President Barack Obama, which was published yesterday, showed a lack of understanding of Iranian politics.
"Recent declarations from the the White House show that some US officials do not have a correct and realistic assessment of the situation here and the message that the Iranian people gave in the election," Rouhani said.
On Sunday, the White House said Iran will find the United States a "willing partner" if Rouhani is prepared to engage substantively and seriously on its nuclear programme.
In a message congratulating Rouhani on his inauguration, the White House said it "presents an opportunity for Iran to act quickly to resolve the international community's deep concerns over Iran's nuclear programme.