The Ukrainian president also accused Russia of “significantly increasing” its offensive despite the peace agreement reached in Minsk on February 12.
Meanwhile, the US said it was very concerned by reports of heavy weapons coming across the border from Russia.
Shelling was heard in the rebel-held city of Donetsk early on Saturday, February 14.
Fierce battles are also said to be continuing around Debaltseve, a strategic government-held town almost encircled by rebel forces.
More than a dozen civilians are said to have died in shelling in eastern Ukraine on February 13.
It is unclear who was behind the shelling but both the Ukrainian military and pro-Russian rebels in the eastern Donetsk and Luhansk regions accuse each other of targeting residential areas.
France President Francois Hollande, Russian President Vladimir Putin and Ukrainian President Petro Poroshenko as well as German Chancellor Angela Merkel – who together clinched the agreement in the Belarusian capital – are due to discuss the issue by phone over the weekend.
The UN Security Council will also meet in emergency session on February 15.
Correspondents say the fighting shows no sign of stopping.
Ukrainian Deputy Defense Minister Petro Mekhed said the rebels wanted to “raise their flag” over Debaltseve and the key port city of Mariupol before the midnight ceasefire kicked in.
“Ukraine is expecting an escalation and taking all necessary measures to be able to respond,” Petro Mekhed told reporters.
Rebel shelling killed two people in a cafe in Shchastya, near Luhansk, on February 13 as well as a child near a school in Artemivsk, a town near Debaltseve, according to Kiev-controlled regional authorities.
Meanwhile, the rebels said at least six people had died in shelling in the city of Donetsk and town of Horlivka. The rebels accuse government forces of shelling the towns.
“After what we achieved in Minsk this is not just shelling of Ukrainian civilians and residential neighborhoods – this is an attack on our Minsk achievements, without any explanations,” President Petro Poroshenko said.
“Unfortunately, after Minsk, Russia’s offensive operations have intensified,” he said, before adding: “We are still convinced that the Minsk achievements are in a big danger.”
There were also reports of a government offensive near Mariupol, the city between rebel-held eastern areas and the southern Crimea peninsula, which was annexed by Russia last March.
Pro-Russian rebels signed the peace agreement but key issues remain to be settled, including the situation in Debaltseve.
European leaders have warned Russia that it could face additional sanctions if the agreement is not respected.
German Chancellor Angela Merkel said the deal offered “a glimmer of hope”, but warned: “It is very important that words are followed by actions.”
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