Petro Poroshenko's personal letter and US Secretary Jack Lew's warning to Putin came one day after European Union leaders unanimously backed pursuing more economic restrictions against Russia for its alleged meddling in Ukraine.
Western sanctions and a coinciding slide in the price of its vital oil exports have sent Russia into recession and seen Standard and Poor's slap a "junk" rating on Moscow's foreign currency debt.
The downgrade threatens to further alienate Western investors from Russia and assigns the economy with a failing grade not seen since the onset of Putin's 15-year rule.
The pro-Moscow rebels last week defiantly pulled out of peace talks and vowed to overtake a strategic coastal Ukrainian city that could provide a direct land bridge between the Russian border and Ukraine's Russian-occupied Crimea peninsula.
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The fighters later denied killing 30 civilians in a weekend rocket assault on the port of Mariupol that international monitors said was launched from rebel-held territory.
A new eastern offensive has also seen the separatists of the Lugansk and Donetsk regions try to link up their armies by taking over isolated pockets of land still controlled by government troops.
Poroshenko's office said the letter to Putin demanded that Moscow immediately rein in the rebel offensive and fulfil the terms of a long-ignored September peace plan it signed with Kiev and two top separatist leaders in Belarus.
"On Monday, I sent a letter to President Putin whose main elements included not only the demand to cease fire and implement the Minsk Agreements but also to release Nadezhda (Nadia) Savchenko and all the hostages," the presidency quoted Poroshenko as saying.