Russian President Vladimir Putin showed no signs of bending to world leaders' warnings about his military intervention in Ukraine on Monday, as pressure grew on President Obama to take measures to punish Moscow.

Reports said Russian troops ordered the crews of two Ukrainian warships to surrender by 10 p.m. EST or be seized by force.

Russia now controls all Ukrainian border posts in the Crimean region, along with a military base and a key ferry terminal, strengthening their hold on the area, the Associated Press reported Monday along with the disputed reports that Moscow demanded that Ukraine give up the warships.

A member of the Russian Black Sea fleet denied the threat to storm the Ukrainian warships, telling AFP that the reports are “complete nonsense.”

Amid the confusion, the Obama administration is reportedly moving swiftly to prepare sanctions on Russia.

The Crimean Peninsula hosts the Russian Black Sea Fleet under a prior agreement with Ukraine, and Russian warships far outnumber Ukrainian vessels in the area. Obama administration officials said Sunday they believed Russian is now dominating control of Crimea with approximately 6,000 troops on the ground there.

Obama, who had a pre-scheduled meeting with Israeli Prime Minister Benjamin Netanyahu Monday at the White House to check in on the Israeli-Palestinian peace talks, is facing one of his biggest foreign policy tests to date as hawkish foreign policy experts push him to take stronger actions against his own studied anti-interventionist tendencies.

While no one in Washington is calling for a direct U.S. military intervention in the conflict, some national security experts on the right say it's time to provide military assistance to Ukraine and move U.S. naval warships into the Black Sea to allay concerns in the Balkans about Moscow's aggression.

“It's time to up the ante a bit,” Gary Schmitt, co-director of the Marilyn Ware Center for Security Studies at the American Enterprise Institute, told reporters on a conference call Monday. “The Ukraine needs anti-air capability and anti-tank capability and [help with] intelligence activities.”

Schmitt also said it's time for NATO to mobilize “rapid reaction forces” in coordination with the Balkan states “to make sure there is a line that Russia can't go beyond” and for the U.S. to deploy naval warships to the Black Sea “to remind Russia there is a cost for its activities.”

The growing fears over regional instability were highlighted Monday when NATO scheduled a Tuesday meeting after Poland, fearing its territorial integrity and political independence could be threatened, requested the security group confer.

“The developments in and around Ukraine are seen to constitute a threat to neighboring Allied countries and having direct and serious implications for the security and stability of the Euro-Atlantic area,” NATO said in a statement Monday afternoon.

Military actions should be taken, Schmitt said, along with several economic measures to make it difficult for Russian companies to do business throughout the world, including visa bans on “Russian elites” and freezing Russian bank accounts abroad. He also suggested it would be worthwhile to go to the United Nations and attempt to pass a resolution condemning Russia's violation of Ukraine's sovereignty even though Moscow would immediately veto it.

“The fundamental policy goal has to be making the Russians see that Putin has overplayed his hand — that the costs of his actions have to be greater than his rewards,” he said.

The latest Russian provocation came as members of the European Union foreign affairs council are meeting Monday, and U.S. Assistant Secretary of State Victoria Nuland attends a meeting of the Organization for Security and Cooperation in Europe.

Secretary of State John Kerry is traveling to Kiev for meetings Tuesday, and Vice President Joe Biden called Russian Prime Minister Dmitri Medvedev on Monday morning to urge him to pull back troops.

Russian Foreign Minister Sergey Lavrov, during a U.N. meeting in Geneva, said Russia was simply defending the human rights of Russian-speaking citizens in Crimea.

“This is a question of defending our citizens and compatriots, ensuring human rights, especially the right to life,” he said, according to reports.

This story was published at 1:33 p.m. and has been updated.