The olive branch came as the clock ticked down to a deadline tomorrow for the separatists to walk out of the state security building in the eastern city of Lugansk and the seat of government in nearby Donetsk or face the possible use of force.
The armed assailants want the heavily Russified east of the culturally splintered ex-Soviet nation to hold independence referendums like the one that led to Moscow's annexation of Crimea last month.
Acting President Oleksandr Turchynov, in power since the February 22 ouster of a pro-Russian leader but deemed illegitimate by the Kremlin, told lawmakers that Ukraine's latest secessionist crisis could be resolved peacefully.
"If people lay down their arms and free the administration buildings, we guarantee that we will not launch any criminal proceedings against them. I am ready to formalise this in a presidential decree," said Turchynov.
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Many in Ukraine's southeast are wary of the more nationalist leaders who rose to power in Kiev. They have been looking to Putin for help.
The militants holed up inside the Donetsk government seat were busy today fortifying their barricades with razor wire and old tyres that could be set on fire in case of a police assault.
The negotiations in Donetsk have involved some of Ukraine's most powerful security officers as well as its richest tycoon.
"They are working on a peaceful solution, and this fills us with optimism," said First Deputy Prime Minister Vitaliy Yarema.
Both Washington and EU nations have accused the Kremlin of orchestrating the unrest in the east in order to have an excuse to invade the region, a charge denied by Moscow.