WASHINGTON—The Obama administration is trying to unilaterally ratchet up pressure on Russia as it leans on global powers to back harsher sanctions should Moscow continue to stir trouble in Ukraine.

At the same time, a set of weekend meetings in Washington of the International Monetary Fund and the World Bank showcased the reluctance of European allies to impose stronger measures against Moscow. Concern runs high in Europe about the economic repercussions of penalizing a major trading partner and energy supplier.

The U.S. moves come amid signs of an escalation by Russia, as pro-Russian forces apparently backed by Russian agents have taken over several cities and towns in the east.

Sen. John McCain (R-Ariz.). a frequent critic of the Obama administration, said the escalation resulted from the failure of the U.S. "to enact anything really meaningful or important" following Russian President Vladimir Putin's encroachment into Crimea.

"It's obvious that he is encouraged by the fact that we sanctioned a few people and suspended—didn't even throw him out—of the G-8," Mr. McCain said on CBS television.