Russian Prime Minister Dmitry Medvedev says Moscow may cut diplomatic ties with Kiev, after President Vladimir Putin accused Ukraine of trying to carry out 'terrorist attacks' in Crimea.

"This is act of sabotage; in essence, a crime which should be investigated according to the set procedure, and the persons involved as well as organizers should be liable to responsibility, criminal responsibility. As far as cutting diplomatic ties, I would not want it to end this way. But if there is no other way to influence the situation, the president could probably take such a decision," Dmitry Medvedev said.

Medvedev's announcement came after Ukraine put its troops on combat alert along the country's de-facto borders with Crimea on Thursday, amid an escalating war of words with Russia over Crimea.

Earlier this week, the Ukrainian Foreign Minister also spoke of the possibility of breaking diplomatic ties with Moscow, but said Kiev would not want that because it would mean abandoning the four million Ukrainians who live and work in Russia. In March 2014, Crimea left Ukraine and joined Russia following a hasty referendum.