The move added to a flurry of signals that the West is bracing for an aggressive Russian move against Ukraine, though Moscow denies any plan to invade.
"I welcome allies contributing additional forces to NATO," the Western military alliance's Secretary-General Jens Stoltenberg said in a statement. "NATO will continue to take all necessary measures to protect and defend all allies, including by reinforcing the eastern part of the alliance."
Britain said it was withdrawing some staff and dependants from its embassy in Ukraine in response to "a growing threat from Russia", a day after the United States said it was ordering diplomats' family members to leave.
"Military action by Russia could come at any time," the U.S. Embassy said in a statement. Officials "will not be in a position to evacuate American citizens in such a contingency, so U.S. citizens currently present in Ukraine should plan accordingly," it added.
U.S. diplomats at the embassy in Kyiv were being allowed to leave voluntarily.
The tensions over Ukraine have contributed to a rise in oil, with the latest Russia-U.S. talks on Friday failing to produce any big breakthrough.
Russia is demanding that NATO withdraw a promise to let Ukraine join one day, and that the alliance pull back troops and weaponry from former Communist countries in eastern Europe that joined it after the Cold War.
Washington says those demands are non-starters but it is ready to discuss other ideas on arms control, missile deployments and confidence-building measures.
The United States and the European Union have warned Russia not to invade Ukraine. Denmark said the EU was ready to impose "never-seen-before" economic sanctions and EU foreign ministers meeting in Brussels said they would send a unified warning to Moscow.