Russia is to reinforce its troop deployments in annexed Crimea and southern Russia because of the worsening crisis in Ukraine and the buildup of foreign forces nearby, the country's defence minister said on Tuesday.

Sergei Shoigu told a meeting of defence ministry top brass it was a "priority" to deploy a "full and self-reliant group of troops in the direction of Crimea," Russian news agencies reported.

He said the "situation in Ukraine has sharply worsened and the foreign military presence has increased very close to our border".

Shoigu said the "military and political situation" in southwest Russia had "changed significantly since the start of this year."

Russia is deeply concerned at NATO's move eastwards and President Vladimir Putin has accused the West of provoking the crisis in Ukraine in order to "revive" the military bloc.

NATO this month agreed to set up a new rapid response force that would be ready to deploy within a few days and also to maintain a "continuous presence" in its eastern member states.

Putin said last month that it was necessary to "implement all of the country's defence measures fully and promptly, including of course in Crimea and Sevastopol, where we have to de facto create military infrastructure from scratch".

Russia's Black Sea fleet is based in Crimea and Moscow announced in July that it had begun expanding and modernising it with new ships and submarines.

Putin ordered the annexation of Crimea from Ukraine in March, saying later he had righted a wrong by reclaiming a peninsula that used to belong to the Soviet republic of Russia before 1954.

Over the weekend Crimea's residents joined Russians across the country in voting in the first local elections since the peninsula's takeover.

In Sunday's elections to the Crimean regional parliament, Russia's ruling United Russia party won more than 70 percent of the vote, while the ultra-nationalist Liberal Democratic Party of Russia received just under 8.5 percent.

Kremlin-friendly analysts said the results showed that Crimea's residents conclusively backed joining Russia.

The United States on Monday rejected the Crimean polls as illegitimate.

"The United States does not recognise the legitimacy of the so-called local and regional elections in Crimea on September 14 and will not acknowledge their outcome," State Department deputy spokeswoman Marie Harf told reporters.

"Our position on Crimea remains clear: the peninsula remains an integral part of Ukraine," she said.