There has been fresh shelling near Donetsk airport in eastern Ukraine, raising fears that a 36-hour-old ceasefire is near to collapse.
The truce held for much of Saturday but overnight shelling in Mariupol was followed by the explosions near Donetsk airport early on Sunday.
The truce and 12-point peace roadmap was signed at talks involving Ukraine, Russia, the rebels and the OSCE.
Fighting in the east has left some 2,600 people dead since April.
Russia has repeatedly denied accusations by Ukraine and the West that it has been sending regular troops into eastern Ukraine to help the rebels, who want to establish an independent state.
Before the ceasefire was agreed in Minsk, Belarus, on Friday, the separatists had been advancing on both Donetsk airport and Mariupol, a key city on the route to Crimea and an economic prize for any possibility of independence for the eastern Ukraine region.
The presidents of Ukraine and Russia both said on Saturday that the truce was largely holding.
However, late on Saturday, eyewitnesses said pro-Russian rebels had shelled and destroyed a government checkpoint on the eastern approaches to Mariupol.
One Ukrainian soldier told Reuters that government forces had pulled out tanks in line with the truce.
He said: “We only left lightly armed people to man checkpoints and these monsters violated every word of the agreement.”
However, separatist leader Andrei Purgin told Russia’s RIA news agency: “Despite the provocations of Ukrainian forces, the militias… will keep firmly to the Minsk agreement. The militias are not resorting and will not resort to arms.”
One Mariupol resident told Agence France-Presse: “I’m frightened. I want peace but I think this ceasefire is finished; this is the third night we haven’t been able to sleep.”
The fighting died down overnight in Mariupol but explosions were then heard on Sunday morning near Donetsk airport.
One rebel fighter told Reuters: “Listen to the sound of the ceasefire. There’s a proper battle going on there.”
The airport has been under the control of government troops since May but has been under constant rebel attack.
Separately, a new report by Amnesty International accuses all sides in the conflict of committing war crimes.
The human rights group said civilians had accused Ukrainian government troops of shelling their neighbourhoods indiscriminately.
Witnesses also said that separatist fighters had “abducted, tortured, and killed their neighbours”. The report accused Russia of fuelling separatist crimes.