Two teenagers died and four were wounded when an artillery shell hit a school playing field as they played football in eastern Ukraine.
The attack in Donetsk came as both sides in the Ukrainian conflict accused each other of tearing up a peace deal.
A fragile ceasefire has been in place since 5 September, although hundreds of people have been killed since then.
Fighting erupted in April after pro-Russian separatists seized control in the regions of Donetsk and Luhansk.
More than 4,000 people have died in eastern Ukraine since the conflict began and the European OSCE monitoring mission has warned that the "bloodletting" is still going on, with numerous incidents of shelling.
The shell landed close to Donetsk airport at a school which was rebuilt by one of Ukraine's richest men, steel billionaire Rinat Akhmetov, and reopened last year.
The head of Mr Akhmetov's humanitarian fund, Rimma Fil, told the BBC that the children had been playing football after lunch when the shell exploded on the pitch.
The four wounded teenagers were being treated in intensive care, she said. Mr Akhmetov described the attack as a terrible tragedy and appealed for an end to the violence.
Shelling in Donetsk intensified on Tuesday night and there were reports earlier on Wednesday of one civilian killed and several others wounded in mortar attacks.
The area around Donetsk airport has seen some of the worst violence in the weeks since the ceasefire was declared. Ukrainian forces have been holding out at the airport despite a siege by the separatists.
Four adults were killed at another school near the airport a month ago, on the day children returned to school after an extended summer break.
Fears of a return to full-scale conflict were raised after the rebels held elections on Sunday in defiance of the government in Kiev and Western countries.
President Petro Poroshenko accused them of tearing up the Minsk peace deal and he said a law granting the rebel-held regions partial autonomy would be scrapped. He has ordered reinforcements to key cities in case of a rebel offensive.
But the separatists hit back on Wednesday, arguing that it was the scrapping of the special status deal that broke the peace agreement.
Although Mr Poroshenko insisted he had not given up on the peace plan, he said Ukraine had to "repel possible attacks" and not allow the "spread of this cancerous tumour".
Russia has recognised Sunday's vote which led to separatist leader Alexander Zakharchenko, 38, being sworn in as head of the self-declared Donetsk People's Republic.
Igor Plotnitsky, a 50-year-old ex-Soviet army officer, was declared head of the self-proclaimed Luhansk People's Republic, further to the east.
But Ukraine and the EU say the vote should have been held on 7 December and run by the central government in Kiev. Germany said Russia's recognition of Sunday's "extremely questionable" poll was "incomprehensible".
Nato Secretary-General Jens Stoltenberg said on Tuesday that Russian troops had recently been seen moving closer to the border with Ukraine and Moscow was continuing to train the separatists. There have also been reports of troop movements within rebel-held areas.
Talks aimed at salvaging the truce took place in Donetsk on Wednesday, involving the rebels and military officials from Kiev and Moscow. An OSCE spokesman told AFP news agency that the level of confidence was very low but it was encouraging that they were still talking.
While the Minsk deal risks unravelling, the first part of an agreement reached last Friday to resume Russian gas supplies to Ukraine has gone through.
Russian state-owned gas giant Gazprom said it had received $1.54bn (£970m; €1.2bn) from Ukraine's Naftogaz, the first instalment of a $3.1bn payment of debt for gas dating back to late last year. Ukraine's gas supplies were turned off in June in a row over unpaid bills and a sharp increase in gas prices.
Russia annexed Ukraine's southern Crimea peninsula in March, after protesters in Kiev ousted pro-Russian President Viktor Yanukovych from power, prompting separatists to take over the Donetsk and Luhansk regions in the east.
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