TALLINN, Estonia -- President Obama proclaimed an unwavering and permanent U.S. commitment to the security of its NATO allies, as he mounted a show of solidarity Wednesday with European nations anxious about Russia's aggression in Ukraine.

During a visit to Estonia, Mr. Obama also announced the U.S. would send more Air Force units and aircraft to the Baltics, and called Estonia's Amari Air Base an ideal location to base those forces.

Standing shoulder to shoulder with Estonian President Toomas Hendrik Ilves at a joint news conference, Mr. Obama ticked through a list of U.S. military resources already at work in the region, and said the U.S. has a duty under the NATO charter to the alliance's collective defense.

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"It is unbreakable, it is unwavering, it is eternal. And Estonia will never stand alone," Mr. Obama said in Tallinn, Estonia's port capital.

Mr. Obama's firm words came as NATO nations were preparing to commit to a more robust rapid-response force for the region, in response to Russia's incursion in Ukraine. Moscow's moves have sparked fears among member states on NATO's eastern flank that they could be Russian President Vladimir Putin's next target.

Shortly after Mr. Obama arrived in Europe, the office of Ukrainian President Petro Poroshenko said he and Putin had reached agreement on a cease-fire -- an unexpected development that added further uncertainty to Mr. Obama's meetings with regional leaders. Later, though, his office retracted the statement, saying it went too far in describing a phone call between the two leaders, the New York Times reports.

Mr. Obama said it was too early to tell what the word of a cease-fire mean, reports CBS News chief White House correspondent Major Garrett, who is traveling with the president. At almost the same time, Moscow said there was no cease-fire, because Russia isn't party to the conflict with Ukraine.

Garrett said that lent credence to the president's statement later that it was not his job to interpret Putin's psychology. There is great concern in Estonia that Russia's next military move could be on Estonia.

Mr. Obama said NATO would would live up to its requirement to defend any NATO member from military attack.

The president said economic sanctions so far have imposed real and painful costs on Russia and would continue as long as Moscow continues to violate basic principles of international law.

Ilves, reacting to word of the cease-fire, said wryly, "I just hope it works."

The Estonian leader cautioned that for a cease-fire to be successful, Russia would have to acknowledge its own participation in the conflict - a step Moscow has previously refused to take. After a meeting with Poroshenko last week, Putin had said a cease-fire was not discussed because Russia was not a party to the conflict.

"This is aggression," Ilves said. "Russia must admit that it is a party to the conflict."

He called for "a robust and a visible ally presence here in Estonia," arguing that such a presence would be the best way to deter any potential aggressors in the region -- a clear reference to Russia.

Also, the Reuters news agency reports that a pro-Russia rebelleader in the Donbass region of eastern Ukraine said Wednesday the withdrawal of Ukrainian forces from "our territory" was the main condition for peace in the separatist-held area.

According to Reuters, Vladimir Antyufeyev, deputy prime minister of the self-proclaimed Donetsk People's Republic, told it by phone that talk of a Russia-Ukraine truce was a "provocation" because Russia isn't a party to the conflict.

At the news conference, Mr. Obama held up Estonia as an example of how every member of the military alliance needs to do its fair share for the collective defense of all 28 members. The U.S. and Estonia are two of four NATO countries that fulfill their pledges to contribute 2 percent of their GDP to defense spending.

He also spoke to the people of Estonia following the press conference, and pledged in no uncertain terms that NATO would stand by the Baltic nations to ensure their security.

"We'll be here for Estonia. We will be here for Latvia. We will be here for Lithuania. You lost your independence once before. With NATO, you will never lose it again."

Later Wednesday, Mr. Obama and Ilves were held broader security talks that include the leaders of Latvia and Lithuania. Then Mr. Obama departs for Wales, where a two-day NATO summit will begin on Thursday.

NATO allies plan to agree during the summit to a stepped-up response to Russia, including the rapid response force, which will involve positioning more troops and equipment in the Baltics and elsewhere in Eastern Europe. It's unclear whether the plan will satisfy the concerns of the Baltic nations, who have been pressing NATO for permanent bases in the region.

After arriving in Tallinn on a crisp and sunny morning, Mr. Obama was greeted by Ilves at Kadriorg Palace, where Mr. Obama placed his hand over his heart as the U.S. national anthem played. The two leaders then inspected Estonian troops and shook hands with groups of flag-waving schoolchildren.

Mr. Obama becomes the second sitting American president to visit Estonia, following President George W. Bush, who traveled here in 2006. As he entered the palace, Mr. Obama wrote in a guest book that it was an honor to visit "a nation that shows what free people can achieve together."

The Baltics were invaded by the Soviet Union and Nazi Germany during World War II. After the Soviet Union crumbled, the Baltic countries turned to the West and joined the European Union and NATO in 2004, much to the chagrin of Russia.