"We've made enough progress in the last days to merit staying until Wednesday. There are several difficult issues still remaining," State Department spokeswoman Marie Harf said.
The announcement came late on a sixth day of talks in Switzerland aimed at laying the groundwork for a deal that world powers hope will prevent Iran developing nuclear weapons under the guise of its civilian programme.
The stakes are high, with fears that failure to reach a deal may set the United States and Israel on a road to military action to thwart Iran's nuclear drive, which Tehran says is purely peaceful.
A German diplomatic source also said the talks were "difficult" with a "changeable atmosphere" and "frequent breaks to negotiate in smaller groups".
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A Western diplomat said the army of technical and sanctions experts would continue plugging away "for (the) next hours. All parties (are) working hard and (are) committed to finding a solution."
Senior Iranian negotiator Hamid Baidinejad said: "The negotiations will end when solutions have been found... We are ready to continue. We are not watching the clock."
Under a deal to be finalised by June 30, the powers want Iran to scale back its nuclear programme to give the world ample notice of any dash to make the bomb by extending the so-called "breakout" time.
In return, the Islamic republic is demanding the lifting of sanctions that have strangled its economy.
But the question is how much detail will be in the framework accord that Iran and the six powers -- the US, China, Russia, Britain, France and Germany -- want to leave Lausanne having secured.