Ukraine's President Petro Poroshenko has ordered army reinforcements to key southern and eastern cities, in case of a new rebel offensive.
Mr Poroshenko made the announcement after meeting security chiefs in the wake of elections in rebel-held areas of Donetsk and Luhansk regions.
He said he was committed to the current peace process, but has proposed cancelling a key plank of the plan.
The peace process was laid out in a September 5 ceasefire deal.
It follows the swearing in of the leader of separatist rebels in eastern Ukraine after an election that was roundly condemned by the West as destabilising.
Alexander Zakharchenko was inaugurated in a heavily guarded theatre in the main rebel stronghold of Donetsk.
His election was largely a formality as no viable candidates opposed him, but separatist authorities have held up the vote as a mandate to pursue their secessionist goals.
The inauguration coincided with Russia's National Unity Day holiday, which saw rallies throughout the country, including one in Moscow that police estimated at 75,000 participants.
The march in the centre of the capital included banners reading “Crimea is ours” – the Ukrainian region annexed by Russia in March – and “Novorossiya - we are with you”. The separatist Ukrainian regions are widely referred to by that name, which means “New Russia” and reflects a widespread opinion that eastern Ukraine is historically and ethnically part of Russia.
The rally in central Moscow incorporated mainstream political groupings, but hardline nationalists held a separate march of several thousand in the suburb of Lyublino. Police arrested several demonstrators there who tried to light fires.