President Vladimir Putin ordered troops involved in a military exercise in western Russia back to base on Tuesday in an announcement that appeared intended to ease East-West tension over fears of war in Ukraine.

Russian financial markets rebounded after sharp falls on Monday, and the euro and dollar rose in Japan, though Moscow's forces remained in control of Ukraine's Crimea region, seized bloodlessly after Russian ally Viktor Yanukovich was ousted as Ukrainian president last month.

Russia paid a heavy financial price on Monday for its military intervention in Ukraine, with stocks, bonds and the rouble plunging as Putin's forces tightened their grip in Crimea, whose population is mainly ethnic Russian.

The Moscow stock market fell 10.8 percent on Monday, wiping nearly $60 billion off the value of Russian firms, but Russian stock indexes rose more than 4 percent early on Tuesday before slipping back again slightly, though still up on the day.

Putin declared at the weekend that he had the right to invade Ukraine to protect Russian interests and citizens after Yanukovich's downfall following months of popular unrest. Russia's Black Sea Fleet has a base in Crimea.

But the military exercises in central and western Russia, which began last week and raised fears that Russia might send forces to neighbour Russian-speaking regions of east Ukraine, were completed on schedule.

"The supreme commander of the armed forces of the Russian Federation, Vladimir Putin, gave the order for the troops and units, taking part in the military exercises, to return to their bases," Kremlin spokesman Dmitry Peskov was quoted as saying by Russian news agencies.

Although the end of the exercises had been planned, the announcement sent a more conciliatory message than much of the rhetoric from Russian officials, who say Moscow must defend national interests and those of compatriots in Ukraine.

Putin is dismayed that the new leadership in Ukraine, the cradle of Russian civilisation, has plotted a course towards the European Union and away from what had been Moscow's sphere of influence during generations of Soviet Communist rule.

Moscow's UN envoy told a stormy meeting of the Security Council that Yanukovich had sent a letter to Putin requesting he use Russia's military to restore law and order in Ukraine. - Reuters