WASHINGTON — As Russia dispatched more forces and tightened its grip on the Crimean Peninsula on Sunday, President Obama embarked on a strategy intended to isolate Moscow and prevent it from seizing more Ukrainian territory even as he was pressured at home to respond more forcefully.

Working the telephone from the Oval Office, Mr. Obama rallied allies, agreed to send Secretary of State John Kerry to Kiev and approved a series of diplomatic and economic moves intended to “make it hurt,” as one administration official put it. But the president found himself besieged by advice to take more assertive action.

“Create a democratic noose around Putin’s Russia,” urged Senator Lindsey Graham, Republican of South Carolina. “Revisit the missile defense shield,” suggested Senator Marco Rubio, Republican of Florida. “Cancel Sochi,” argued Representative Mike Rogers, the Michigan Republican who leads the Intelligence Committee, referring to the Group of 8 summit meeting to be hosted by President Vladimir V. Putin. Kick “him out of the G-8” altogether, said Senator Richard J. Durbin of Illinois, the Democratic whip.

The Russian occupation of Crimea has challenged Mr. Obama as has no other international crisis, and at its heart, the advice seemed to pose the same question: Is Mr. Obama tough enough to take on the former K.G.B. colonel in the Kremlin? It is no easy task. Chancellor Angela Merkel of Germany told Mr. Obama by telephone on Sunday that after speaking with Mr. Putin she was not sure he was in touch with reality, people briefed on the call said. “In another world,” she said.