Putin had said his request, made a day earlier, was intended to help support the peace process in Ukraine, which began Friday with a weeklong cease-fire.
Putin needs to show his support for Ukrainian President Petro Poroshenko's peace plan ahead of Friday's European Union summit to avoid further Western sanctions. The EU has warned it could introduce new sanctions that would target entire sectors of the Russian economy if Moscow fails to help de-escalate the crisis.
The vote came as NATO foreign ministers gathered in Brussels, warning that more sanctions were possible and considering ways to bolster Ukraine's military.
German Chancellor Angela Merkel told lawmakers Wednesday that Putin's move to rescind the permission for using military force in Ukraine was an "important psychological point," but that progress toward a solution remains slow and EU is still prepared to increase sanctions.
Merkel, who was set to have a phone call with Putin, French President Francois Hollande and Poroshenko later in the day, said the EU will do everything possible to help find a diplomatic resolution, but added that "if nothing else helps, sanctions could return to the daily agenda, and this time at the third level."
Two previous rounds of U.S. and EU sanctions imposed asset freezes and travel bans on members of Putin's inner circle over Russia's annexation of Crimea. The next round, which would impose penalties for entire sectors of the Russian economy, could be far more crippling.
Maintaining pressure on the Kremlin, NATO's secretary general said Wednesday there are "no signs" Russia is respecting its commitments over Ukraine.
"So today we will review our relations with Russia and decide what to do next," Anders Fogh Rasmussen said as he arrived for the foreign ministers meeting.
Rasmussen said foreign ministers also would discuss how NATO can help build Ukraine's military capacities, including by creating trust funds.
As outlined by an alliance official, who spoke on condition of anonymity because no official decision has been reached, the trust funds for Ukraine would not bankroll the acquisition of lethal hardware, but would help pay for improving the former Soviet republic's capabilities in areas like logistics, cyberdefense and command and control of military forces, as well as the resettling of soldiers whose barracks had been closed.
On Tuesday, Putin urged Ukraine to extend the truce and sit down for talks with the rebels. He argued that the Ukrainian demand that the insurgents lay down their weapons within a week was unrealistic, explaining that they would be reluctant to disarm for fear of government reprisals.
The Russian leader also called on Ukraine to adopt constitutional amendments and other legal changes that would protect the rights of Russian-speakers in the east.
Poroshenko said Wednesday that he would submit draft constitutional amendments offering broader powers to the regions and hoped for quick approval by parliament.
The cease-fire has been repeatedly broken by sporadic clashes, and it was violated again Tuesday when rebels used a shoulder-fired missile to down a Ukrainian military helicopter, killing nine servicemen. The attack, which came a day after the rebels pledged to respect the cease-fire, prompted Poroshenko to warn that he may end the truce ahead of time.
British Foreign Secretary William Hague hailed Poroshenko's peace plan and pointed at the helicopter's downing as an evidence of a lack of support from Russia.
"We urge Russia to take the necessary actions to stop the flow of arms across the border, to stop supporting illegally armed separatist groups in Eastern Ukraine, because in absence of actions by Russia the case for stronger sanctions from European Union nations will of course become stronger," Hague said.
Putin's March 1 request to parliament for authority to use the military in Ukraine came days after Ukraine's pro-Russian president was chased from power following months of street protests. Russia sent troops that quickly overran Ukraine's Black Sea peninsula of Crimea, setting the stage for Russia to annex it after a hastily called referendum.
In April, a mutiny erupted in eastern Ukraine, where pro-Russian insurgents seized official buildings, declared their regions independent and fought government troops. The U.S. and NATO accused Russia of supporting the rebellion with troops and weapons, but Moscow has denied that.
John-Thor Dahlburg in Brussels and David Rising in Berlin contributed to this report.
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