There has been fresh shelling near Donetsk airport in eastern Ukraine, raising fears that a 36-hour-old ceasefire may collapse.
The truce held for much of Saturday but shelling in Mariupol, which killed one woman, was followed by the Donetsk airport blasts 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.
Local officials said one 33-year-old woman civilian was killed and three people injured in the shelling.
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.”