It follows a meeting last night of the five permanent members of the UN Security Council who met for the first time since Russia proposed placing Syria's chemical weapons arsenal under international control.
Discussions between Mr Kerry and Russia's foreign minister, Sergei Lavrov, are scheduled to last two days but could continue until Saturday. It comes a day after Russia handed over its proposals for dealing with Syria's chemical weapons, and President Barack Obama's delaying of a congressional vote on air strikes against Syria in order to seek a diplomatic alternative.
Mr Kerry will be accompanied in Geneva by a team of US arms experts tasked with examining the details of the plans.
A State Department spokeswoman said Russia had so far only "put forward ideas". She added: "We certainly know there are challenges. There are potentially a large amount of chemical weapons in Syria's stockpile."
A White House spokesman said he expected the diplomatic wrangling to take "some time".
Meanwhile, the five permanent members of the UN Security Council were due to hold talks last night in a bid to reach some agreement on how to progress in light of the latest developments. France, Britain and the US had pressed for a UN Security Council resolution on Tuesday that would impose tough consequences should Damascus fail to hand over control of its banned chemical weapons. Russia had also called a Security Council meeting on Tuesday, but later cancelled.
The five permanent members - the only countries with veto power - have been embroiled in deadlock since the beginning of the civil war in Syria, with Russia and China backing the Assad regime and vetoing any intervention in the conflict to the frustration of France, Britain and the US.
According to reports last night, diplomats had been working round-the-clock to persuade representatives for the Security Council to return to the negotiating table to iron out the wording of a possible resolution on the crisis.
The talks follow the move by President Obama to delay the Congress vote on military strikes against Syria. Mr Obama said he wanted to give diplomacy more time to rid Syria of its chemical weapons arsenal.
In his address to the nation on Tuesday night, the US President still pressed the case for action as a deterrent to further use of chemical weapons and a warning to other countries tempted to use them.
He said: "The images from this massacre are sickening. Men, women and children lying in rows, killed by poison gas, others foaming at mouth, gasping for breath, a father clutching his dead children, imploring them to get up and walk."
But he said he would give the proposal by Syria's ally Russia to stockpile the weapons a try.
Polls show a majority of Americans want no more US military involvement in the Middle East after the wars in Iraq and Afghanistan.
"It's too early to tell whether this offer will succeed, and any agreement must verify that the Assad regime keeps its commitments," Mr Obama said. "But this initiative has the potential to remove the threat of chemical weapons without the use of force."
US senators said yesterday that a vote on a resolution to authorise the use of military force against Syria could be held as soon as next week if efforts to find a diplomatic solution fall short, adding that the continued threat of force would pile pressure Syrian President Bashar al Assad.
"There's a strong belief keeping the credible use of military force is very necessary," said Democratic Senator Robert Menendez.