Russia on Friday demanded an apology from Kiev over the "shooting" of a border post from Ukrainian territory as it slammed a ceasefire announcement by Ukraine's Western-backed president.

A Russian checkpoint building was reportedly destroyed by a mortar and one customs official wounded as fighting raged nearby between Ukrainian troops and pro-Moscow rebels.

"The Russian side is waiting for an explanation and an apology in connection with this," the Kremlin press office said according to Russian news agencies.

The foreign ministry in Moscow laid the blame for the "provocation" squarely at the door of Ukrainian government forces.

"Russia expresses a decisive protest in relation to this aggressive act," the ministry said in a statement.

But Ukraine's military denied that it had fired heavy weapons near the border and instead pointed the finger at the insurgents.

"Given the proximity to the state border with the Russian Federation Ukrainian servicemen did not use and are not using artillery or mortars," a statement from the defence ministry said.

The incident came as new Ukrainian President Petro Poroshenko announced a week-long unilateral ceasefire aimed at easing fierce fighting in the east of the country.

But Moscow blasted the latest peace initiative from Kiev and Russian media seized on the reported border shooting to question how genuine the ceasefire offer was.

The Kremlin said the announcement appeared to be little more than a veiled threat to pro-Russian rebels to surrender and said direct talks with the insurgents were needed.

"A first analysis unfortunately shows that it is not an invitation to peace and negotiations but an ultimatum for the militias in the south-east of Ukraine to give up their weapons," the Kremlin press service said.

Daily clashes between separatist insurgents and the country's armed forces have claimed at least 375 lives since a rebel uprising began in April.

Kiev accuses Moscow of being behind the rebellion and has alleged Russia is sending weapons and fighters across its porous border. Russia in turn has accused Kiev of violating the frontier.

Moscow said Friday that it had bolstered its troops near Ukraine to shore up the leaky frontier, as the United States warned that the Kremlin was massing "significant" forces along the border with its ex-Soviet neighbour.

A US official said that some of the Russian troops were "within a handful of kilometres" of Ukrainian territory, "the closest they have been since the invasion of Crimea" earlier this year.

Russian investigators said earlier Friday that they were probing the alleged shooting in the Dolzhansky border area close to where Ukrainian forces had been battling rebel fighters.

The border service in the region said that a mortar had hit the border control building and that all employees had been evacuated from the area, Russian news agency Itar Tass reported.

Local health officials told Russian state television that the injured border employee was undergoing a minor operation to remove some shrapnel and was not in a life threatening condition.