Updated

Key lawmakers backed President Obama’s warning to Russia Friday that "there will be costs" for any military intervention in Ukraine, and offered support for sanctions and other measures aimed at deterring Russia from escalating tensions in the region.

Obama, speaking to reporters at the White House, said that the U.S. government is "deeply concerned" by reports of Russian "military movements" inside Ukraine, warning that any violation of Ukraine's sovereignty would be "deeply destabilizing."

"There will be costs for any military intervention in Ukraine," he said, without specifying what those costs might be.

A bipartisan group of 12 members of the Senate Foreign Relations Committee expressed support for U.S. assistance in Ukraine and raised concerns over the Russian government’s “provocative and dangerous tactics” in response to the upheaval in Ukraine.

“We do not seek confrontation with President (Vladimir) Putin and his government, but simply to ensure that Russia abides by its commitments and adheres to core principles of international law. A peaceful, democratic, stable, and sovereign Ukraine is in our national interest,” the senators wrote.

More On This...

    The lawmakers, which included Sens. John McCain, R-Ariz., Robert Menendez, D-N.J., and Marco Rubio, R-Fla., said they are prepared to work with the Obama administration on imposing “targeted sanctions to “dissuade individuals who would foment unrest to undermine Ukraine's territorial integrity .”

    “We are gravely concerned about the future of Ukraine and are committed to working with you to support a peaceful political transition that serves the interests of the Ukrainian people who have demanded that their voices be heard,” the lawmakers wrote.

    Obama’s warning to Russia on Friday came amid reports that suspected Russian soldiers had landed at a military base in the Crimean peninsula. Officials told Fox News they see "evidence of air and maritime movement into and out of Crimea by Russian forces."

    Later Friday, Mike Rogers, chairman of the House Select Committee on Intelligence, issued a statement saying, "It appears that the Russian military now controls the Crimean peninsula.  This aggression is a threat not only to Ukraine, but to regional peace and stability.  Russia’s latest action is yet another indicator that Vladimir Putin’s hegemonic ambitions threaten U.S. interests and allies around the world."

    A senior U.S. official told Fox News the Pentagon has not prepared "any military contingencies" for Ukraine. Officials say Obama may retaliate by canceling a trip to Russia this summer for an international summit and could also cut off trade discussions with Moscow. But it's unclear whether those moves will have any impact on Russia's calculus in Ukraine.

    The administration is being pressed by members of Congress to act judiciously but firmly, out of concern that Putin is poised to flex his muscle in a bid to exert influence over the volatile power struggle in the former Soviet republic. House Republican Leader Eric Cantor called reports of Russia military movement of "grave concern."

    "It is essential that the United States, our European and NATO partners, and the international community stand up to any aggression," he said. "We need strong American and European leadership now to forestall any further threats to international peace and stability. Russia's leaders must understand that military intervention and further interference in Ukraine's affairs are unacceptable, and would result in significant consequences for Russia."

    Among those consequences, he urged sanctions for "Russian individuals and entities who use force or interfere in Ukraine's domestic affairs."

    Sen. Ted Cruz, R-Texas, warned that Putin would not take Obama’s “vague threats” seriously and urged the administration to consider suspending Russian membership in the World Trade Organization and the United Nations Security Council.

    “The United States should stand with Ukraine,” Cruz said.

    Fox News' Jennifer Griffin and The Associated Press contributed to this report.