Time is running out, however, with Kerry and Mohammad Javad Zarif aiming to agree the outlines of an agreement by the end of the month. A full accord is then due by July 1.
Both men, who began meeting soon after 0700 GMT in a luxury hotel in the lakeside city of Lausanne.Speaking in Egypt before travelling to Switzerland, Kerry sought to ease such concerns, saying that the aim is "not just to get any deal, it is to get the right deal".
"If (Iran's nuclear programme is) peaceful, let's get it done. And my hope is that in the next days, that will be possible," Kerry told CBS television.
There were, however, "important gaps," he said.
"Several questions need to be discussed, those where we haven't found a solution yet and also those where we have found solutions but where we need to discuss certain details," Zarif said on Sunday.
Zarif was later Monday due in Brussels to meet his British, French, German and EU counterparts before returning to Lausanne.
Negotiators from the other five powers involved in the talks -- Russia, China, Britain, France and Germany -- were to be involved from Tuesday, according to Iranian officials.
The impact of Rouhani
The US and Iran have not had diplomatic relations for 35 years but the 2013 election of President Hassan Rouhani resulted in a minor thaw and a diplomatic push to resolve the more than decade-old nuclear standoff.
Under a landmark November 2013 interim deal with the "P5+1" powers,the parties have been pushing for a lasting accord.
Last week 47 Republicans took the unprecedented step of writing an open letter to Iran's leaders.
They warned that any nuclear deal could be modified by Congress or revoked "with the stroke of a pen" by whomever succeeds President Barack Obama, a Democrat.
The Obama administration has been trying to dissuade lawmakers from passing legislation that would force the president to submit any Iran deal to Congress for approval.
Obama is sure to veto this but the Republicans are trying to assemble a two-thirds majority in both houses of Congress with rebel Democrats to pass the measure and override the veto.
'We need clarity'
Some progress has been made towards a deal but the two sides remain far apart on several key issues.
These include the future size of Iran's uranium enrichment capacities -- which can make nuclear fuel also the pace at which sanctions would be lifted and the accord's duration.
"We need clarity on the way in which sanctions will be lifted and what the guarantees will be for applying the deal," Zarif said.
Two deadlines, in July and November, were missed.
"There is no time for additional extensions," Kelsey Davenport, an analyst at the Arms Control Association, told AFP.