Ukraine's defence minister says a new ceasefire has been holding in eastern Ukraine since midnight, despite a recent intensification of shelling.
"This morning I'm pleasantly surprised that at 09:00 (06:00 GMT), since midnight, we haven't had a single shot fired," Stepan Poltorak said.
It is the first time there has been a true halt to fighting in 11 months, says BBC correspondent Tom Burridge.
The truce was agreed with pro-Russian rebels and international mediators.
It marks the start of a new school year in Donetsk and Luhansk.
Eastern Ukraine has seen some of its worst violence for months in recent weeks, and there was heavy shelling last weekend.
On Monday international monitors from the OSCE security organisation reported nearly 1,000 explosions in the Donetsk region in just 24 hours - a big spike in fighting along the front line.
Most took place in an area north of Donetsk airport and between the villages of Avdiivka and Yasynuvata.
The neighbouring Luhansk region also saw a big increase in the number of blasts at the weekend.
Ukraine says massive Russian military exercises near the border have exacerbated tension.
Meanwhile, the UK government has added its voice to international appeals for Russia to release a Crimean Tatar leader, Ilmi Umerov, from a psychiatric unit and give him the medical care he needs. He is reported to be suffering from diabetes and Parkinson's disease.
Russia has prosecuted several key Crimean Tatar activists since its annexation of Crimea in March 2014. The Muslim Tatars, like the Ukrainian government, view Russia's annexation as a flagrant breach of international law.
Rights of children
On Wednesday Ukraine's President Petro Poroshenko said France and Germany - the Western powers that brokered a peace deal in Minsk in February 2015 - had backed Ukraine's call for a ceasefire starting on 1 September.
He said he was awaiting a response from Russian President Vladimir Putin.
Kiev and the West accuse Moscow of arming the rebels and sending Russian regular troops to help them.
The Kremlin denies deploying troops, but admits that Russian volunteers have been fighting alongside the rebels.
A spokeswoman for Ukraine's delegation to the ceasefire talks, Darya Olifer, said more than 150,000 children were attending school in Ukrainian-held areas of Donbass, the industrial region that includes Donetsk and Luhansk.
"We insist that all children in the Donetsk and Luhansk regions, wherever they live, have a right to care and security," she said.
More than 9,500 people - including many civilians - have been killed in the two regions since the pro-Russian insurgents took over a large swathe of territory in April 2014.
Despite the ceasefire agreed in Minsk in February 2015, there have been violations by both sides on an almost daily basis.