World powers are trying to strike a deal with Iran that would prevent Tehran from developing a nuclear bomb in return for an easing of punishing international economic sanctions.
Iran denies its nuclear programme has military objectives.
Kerry finally sat down with Iranian Foreign Minister Mohammad Javad Zarif on Sunday evening after being delayed for several hours in London.
Kerry had time for a quick stroll in the blistering cold along the shores of Lake Geneva as well as briefings with US negotiators before the talks began around 8:30 pm (1930 GMT).
The two men are expected to continue their discussions Monday.
"Tonight's meeting is another step in a long, tough process," a senior State Department official said.
US and Iranian diplomats have been meeting in Geneva since Friday, and senior negotiators from the so-called P5+1 group of Britain, China, France, Russia, the United States and Germany also met with Iranian negotiators Sunday to help drive the talks forward.
There is a heightened sense of urgency as the clock ticks down towards a March 31 deadline to agree on a political framework for the deal.
Kerry warned in London Saturday that "there are still significant gaps, there is still a distance to travel."
But, he added: "President (Barack) Obama has no inclination whatsoever to extend these talks beyond the period that has been set out."
Akbar Velayati, the diplomatic adviser to Iran's supreme leader Ayatollah Ali Khamenei, shot back Sunday that "if American leaders don't want to negotiate, it's up to them, but they were the ones who were after negotiations."
Wang Qun, director general of the arms control and disarmament department of the Chinese foreign ministry, acknowledged that the talks faced "difficulties".
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"We anticipate more difficulties as we move to the final phase," he told reporters in Geneva, while adding "our resolve is greater than the difficulties."
In a sign of the growing push for an accord, US Energy Secretary Ernest Moniz is taking part in the talks for the first time, as is Ali Akbar Salehi, the director of the Iranian Atomic Energy Organisation.
They were both taking part in the talks between Kerry and Zarif Sunday night, and observers suggested their participation was a sign that a deal could be within reach.
Kerry, however, played down the changes in the Iranian camp, saying Moniz was present because of the "technical" nature of the discussions.
While the political aspects of the deal must be nailed down by the end of next month, the deadline for signing the full agreement is June 30 -- a cut-off point that looms all the larger after two previous deadlines were missed.
A key stumbling block in any final deal is thought to be the amount of uranium Iran would be allowed to enrich, and the number and type of centrifuges Tehran can retain.
Under an interim deal reached in November 2013, Iran's stock of fissile material has been diluted from 20 percent enriched uranium to five percent in exchange for limited sanctions relief.
Experts say such measures diminished Iran's ability to make an atomic weapon, which Tehran denies pursuing in the first place.
'DANGEROUS' AGREEMENT FOR ISRAEL AND WORLD
Negotiations have been complicated by hardliners both in Iran and the United States, as well as by Israel lobbying against a deal.
Israeli Prime Minister Benjamin Netanyahu is controversially planning to address the US Congress on the issue on March 3.
The move is aimed at torpedoing a deal. He told a cabinet meeting Sunday that agreeing a deal would "allow Iran to develop the nuclear capabilities that threaten our existence."
Observers stressed the urgency of reaching an agreement and warned that a failure to do so would have dire consequences.
"Another extension is extremely unlikely," Kelsey Davenport, head of the Nonproliferation Policy Arms Control Association in Washington, told AFP.
If no agreement is reached, she warned, both sides will likely head "back down the path of escalation, with Washington increasing sanctions and Iran ramping up its nuclear program."