* RTS crosses 1,400 points for first time since mid-January
* Rouble at multi-month high against euro, dollar (Recasts to reflect new highs, adds comment)
By Alexander Winning
MOSCOW, June 24 (Reuters) - Russian shares and the rouble hit multi-month highs on Tuesday after President Vladimir Putin asked the upper house of Russia's parliament to revoke the right it had granted him to order a military intervention in Ukraine.
The dollar-denominated RTS index was up 2.4 percent at 1,402 points at 1220 GMT, touching its highest since mid-January. The rouble-based MICEX rose 1.3 percent to 1,505 points, reaching levels last seen in mid-February.
The rouble strengthened by 1 percent against the dollar to 33.78. It had earlier reached its strongest since January, getting an extra boost from companies converting foreign currency into roubles before they make monthly tax payments.
"(Putin's) move will calm down Western/Ukraine hawks constantly calling for a threat of Russian invasion," Dmitry Polevoy, the chief economist for Russia and CIS at ING Bank in Moscow, wrote in a note.
"Even though it is difficult to say whether it was a reaction to the remaining threat of extra sanctions ... or simply a strategic play of Mr Putin, it further reduces the probability of tail-risk scenarios in the Ukraine crisis."
On March 1, Russian lawmakers granted Putin the right to use the country's army in Ukraine. Their move drew threats of economic sanctions from the West and prompted a selloff in the rouble and Russian assets.
Equities have since recouped their losses, after Western sanctions turned out to be weaker than were first feared. But the conflict with Ukraine still exerts a powerful influence over the direction of Russia's stock market.
Shares were also supported on Tuesday by reports that pro-Russian separatist leaders in Ukraine's east had agreed to observe a ceasefire with Ukrainian forces, enabling peace talks to proceed.
The rouble firmed by 0.83 percent against the euro to reach 46.02 and also touched a five-month high earlier. Besides the softening stance on Ukraine, Russian exporters are converting foreign currency into roubles to pay a mineral extraction tax on Wednesday.
The Russian currency was 0.92 percent firmer at 39.29 against the rouble-dollar basket the central bank uses to guide the rouble's nominal exchange rate.
In corporate news, U.S. healthcare company Abbott Laboratories said it had agreed to buy Russian drugmaker Veropharm in a deal valued at up to $495 million.
Veropharm's shares were up 35 percent on Monday's close in afternoon trading.
For rouble poll data see
For Russian equities guide see
For Russian treasury bonds see
Russia in graphics: link.reuters.com/dun63s (Reporting by Alexander Winning and Jason Bush; Editing by Larry King)