Rouhani's inauguration gives Iran a chance "to act quickly to resolve the international community's deep concerns over Iran's nuclear programme," White House press secretary Jay Carney said in a statement.
"Should this new government choose to engage substantively and seriously to meet its international obligations and find a peaceful solution to this issue, it will find a willing partner in the US," he said in the message congratulating Rouhani on his inauguration.
Rouhani was officially endorsed by the supreme leader Ayatollah Ali Khamenei yesterday for a four-year term.
In his first public comments after assuming power, Rouhani said, "The only path to interact with Iran is through negotiations on equal grounds, reciprocal trust-building, mutual respect and reducing hostilities".
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"If you want a proper answer, do not speak with Iran with the language of sanctions but with the language of respect," he said, adding Iran would "not surrender to sanctions, nor be threatened with war."
Iran insists that its programme is for peaceful purposes such as power generation and medical purposes only.