"We're moving forward," Mohammad Javad Zarif told reporters after meeting separately with his German and French counterparts who flew into Lausanne, Switzerland on Saturday to join the negotiations.
"I think we can in fact make the necessary progress to be able to resolve all the issues and start writing them down in a text that will become the final agreement once it's done," Zarif said.
France's top diplomat Laurent Fabius, the most hawkish in the P5+1 group of countries negotiating with Iran, said he wanted a "robust deal" with close oversight to ensure no violations.
German Foreign Minister Frank-Walter Steinmeier said the talks had entered their "endgame" but also warned this would also be the hardest stage.
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Russia's chief negotiator, Sergei Ryabkov was quoted by the RIA Novosti news agency as saying the chances of a deal were "more than 50/50".
The powers want Iran to shrink its nuclear programme and impose unprecedented inspections in order to make any covert dash to a bomb all but impossible.
Russian Foreign Minister Sergei Lavrov and Chinese counterpart Wang Yi were reportedly due to join the talks on Sunday. Britain's Philip Hammond was on stand-by.
"It was important that ministers began to arrive... We expect the pace to intensify," a senior US official said.
The Iranians "like to negotiate on the edge of a precipice. They're very good at it," a Western diplomat said.
The deal the negotiators are trying to put together is highly complex and two deadlines last year to turn an interim accord reached in November 2013 were missed.
"Everything is linked. If all the technical issues are resolved and the questions tied to the sanctions are not, then there is no deal," said Iran's nuclear chief Ali Akbar Salehi.