The school is 4km (2.5 miles) from Donetsk airport, where rebels have clashed with Ukrainian troops.
SHAFAQNA- A shell has killed four people at a school in the rebel-held east Ukrainian city of Donetsk, on the first day of classes, officials and witnesses say.
Another six people died when a minibus was hit elsewhere in Donetsk.
No children were apparently hurt when the school playground was shelled but a biology teacher and a parent were among the dead, witnesses told Reuters.
A fragile ceasefire has been in place in eastern Ukraine since 5 September but the truce has frequently been violated.
Both sides blamed the other for Wednesday’s attacks.
The Kiev-controlled regional administration said rebels from the self-proclaimed Donetsk People’s Republic (DPR) had opened fire with a multiple-launch rocket system.
But DPR deputy leader Andrei Purgin told Russian TV that Ukrainian rocket launchers had targeted residential areas from as far as 40km (25 miles) away.
Pro-Russian separatists control of much of Donetsk and have launched several attempts to capture the airport to the north-west of the city in recent weeks.
Ukrainian military spokesman Andriy Lysenko told reporters the airport was still under government control but rebel leader Alexander Zakharchenko told news agencies it would be fully captured in two to three days.
Open conflict began in the east in April, after Russia annexed the Crimean peninsula from Ukraine and pro-Russian separatists then declared independence in the two eastern regions of Donetsk and Luhansk.
Pupils in Donetsk only returned to school on Wednesday after the start of the school year was postponed by a month because of the fighting.
Many children had been moved to safer areas while the fighting was at its heaviest, but although clashes have continued since the ceasefire was declared, the violence has been less widespread.
Well over 200 people were at school number 57 in the Kievsky district when the playground was shelled, including 70 children. Although the school’s windows shattered, none of the children was reported hurt.
Another shell hit a minibus at a bus stop a few streets away from the school and a Reuters reporter described seeing six bodies inside the vehicle.
The BBC’s James Coomarasamy, visiting another school in Donetsk, says far fewer pupils than normal were present for the first day of the year, with the constant echo of artillery in the distance.
“The first thing we should teach our pupils is to love their country and the city they live in and that they should respect the people around them,” an English teacher said.
On his first day as Nato Secretary General, Jens Stoltenberg described the crisis in Ukraine as a major challenge to security and reiterated his predecessor’s strong stance towards Russia.
The Kremlin has denied sending heavy weapons and soldiers to help the rebels but admits that “volunteers” have gone to fight in eastern Ukraine.
“We have to see that Russia changes its behaviour and its actions and returns to compliance with international law and its obligations,” he said. Only a strong Nato could build a constructive relationship with Russia, he added.
The European Commission has written a letter warning Russian President Vladimir Putin not to impose new trade barriers on Ukraine.
As part of a compromise agreed earlier this month, the government in Moscow agreed it would not change its trade provisions with Ukraine if an EU-Ukraine trade accord was put on hold for 15 months.
Commission head Jose Manuel Barroso says a recently adopted Russian decree contravenes that compromise.