The Syrian army, which announced the truce at 1700 BST, said a “regime of calm” would be applied in all of Syria – and that it reserved the right to respond using firepower against any violation by armed groups.
Mr Kerry said it was too early to draw conclusions about how effective the stoppage would be, adding there was no doubt that violations would be reported “here and there”.
Later there was confusion as Mr Kerry suggested the US and Russia could allow the government of Bashar al Assad to target militants linked to al Qaeda.
But the State Department backtracked, with spokesman John Kirby saying: “This is not something we could ever envision doing.”
Violence was reported in several areas in Syria just half an hour before the ceasefire was due to begin.
But after it took effect, the Syrian Observatory for Human Rights said fighting appeared to have stopped in major areas of conflict.
“Calm is prevailing,” said director Rami Abdulrahman.
He added, though, that shelling had been reported by both rebel and government forces in the southwest.
The cessation of hostilities was brokered by the US and Russia – the second attempt this year by Washington and Moscow to bring the five-year civil war to an end.
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Russia, meanwhile, has said “terrorists” will still be targeted.
The Russian Defence Ministry said it would continue air strikes against Islamic State and the former Nusra Front.
It also said a joint US-Russian centre was being set up to to coordinate coalition targets.
The ceasefire will be renewed every 48 hours. If it holds for a week, the US and Russia are due to begin sharing intelligence too.
And it is hoped that humanitarian supplies can be distributed.
In a statement, Russia’s foreign ministry said aid would be delivered to the besieged city of Aleppo straight away.
Mikhail Bogdanov, Russia’s deputy foreign minister, has said peace talks to end the civil war could begin again next month.
Speaking in the Commons the Defence Secretary, Sir Michael Fallon, said the stoppage’s success would depend on whether Russia could rein in the Syrian president, Bashar al Assad.
“Russian military activity in Syria has supported the Assad regime, a regime which bombs, tortures and starves its own people,” Sir Michael said.
“While we welcome the latest ceasefire, it is Russia that must make it work by stopping Assad from attacking Syrian civilians, moderate opposition groups and by helping to get humanitarian aid into Aleppo and other cities that are being starved of food.”
Earlier, President al Assad was pictured praying at a mosque in a Damascus suburb recently taken from rebels.
Touring the district, he said he wanted to recapture the whole of Syria: “The Syrian state is determined to recover every area from the terrorists.
“The armed forces are continuing their work, relentlessly and without hesitation, regardless of internal or external circumstances,” he said in Daraya.
Some rebel groups have expressed concern that the ceasefire is a “trap” which will largely benefit Bashar al Assad’s government.
In a letter to the US, the Free Syrian Army said it planned to “co-operate positively” and respect the ceasefire, but wrote that a lack of enforcement mechanisms and a lack of provision for some of the country’s most besieged areas were worrying.
The FSA also claimed that the exclusion of the Jabhat Fateh al Sham group – a former al Qaeda affiliate known as the Nusra Front – could be used by Russia as a pretext to bomb other rebel groups.
Reacting to its exclusion from the truce deal, a spokesman for Jabhat Fateh al Sham tweeted: “It’s simple – the Russian-American deal is intended to eliminate those who protect Syrians.”
News Source SkyNews