Time is however running short and tempers are fraying in Washington where critics fear that the mooted accord will not do enough to prevent the Islamic Republic getting nuclear weapons.
US Secretary of State John Kerry, due to meet his Iranian counterpart in Lausanne later, sought to allay such concerns, saying the aim was "not just to get any deal, it is to get the right deal".
The target is for Iran and six world powers -- the US, Russia, China, Britain, France and Germany -- to agree the outlines of a deal by March 31 and to fine-tune the details by July 1.
"We believe very much that there's not anything that's going to change in April or May or June that suggests that at that time a decision you can't make now will be made then," Kerry told CBS television.
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If Iran's nuclear programme is indeed "peaceful," as Tehran says, "let's get it done," Kerry said.
The United States and Iran have not had diplomatic relations for 35 years and the standoff over Tehran's nuclear programme has dogged its international relations for more than a decade.
Under a landmark November 2013 interim deal, Tehran stopped expanding its activities in return for minor sanctions relief. Since then the parties have been pushing for a lasting accord.
But to the alarm of Israel and US Republicans, Washington looks to have abandoned insisting that Iran dismantles all nuclear activities, tolerating instead a small programme under tight controls.
In theory, this still leaves Iran with the possibility to get the bomb, critics say, and last week 47 Republicans took the unprecedented step of writing an open letter to Iran's leaders.
This followed a barnstorming address to US lawmakers -- on a Republican invitation -- by Israeli Prime Minister Benjamin Netanyahu warning against a deal.
Republicans have also threatened to bring draft legislation imposing more sanctions towards the end of March, something which would likely prompt Iran to walk away.
The letter provoked a storm in Washington with Vice President Joe Biden calling it "dangerous" and the State Department saying it was "harmful to American security."