“The notion that for us to go forward with sectoral sanctions on our own without the Europeans would be the most effective deterrent to Mr. Putin, I think, is factually wrong,” Mr. Obama told reporters in Asia, where he is traveling. “We’re going to be in a stronger position to deter Mr. Putin when he sees that the world is unified.” He added: “For example, say we’re not going to allow certain arms sales to Russia — just to take an example — but every European defense contractor backfills what we do, then it’s not very effective.”

Some officials, however, privately argue that the administration has made coordinating with Europe too high a priority and that effectively deferring to the 28-member European Union is a recipe for inaction. The United States, these officials contend, should move ahead with more decisive action on the theory that Europe wants leadership from Washington and historically joins in eventually.

“While imposing sanctions together with the E.U. would be nice, the U.S. simply has to lead and not waste more time trying to present a united approach,” said David J. Kramer, president of Freedom House, an advocacy group, and a former Bush administration official, reflecting views expressed inside the government. “It’s easier for us to do so than it is for the Europeans, and they will follow, as long as we lead.”

A task force of Russia specialists that includes Mr. Kramer sent the White House a list of possible sanctions targets, including Russian officials and business leaders as well as nine of its most significant companies.

Senator Bob Corker of Tennessee, the ranking Republican on the Foreign Relations Committee, made a similar proposal. “Hitting four of the largest banks there would send shock waves into the economy; hitting Gazprom would certainly send shock waves into the economy,” he said Sunday on “Face the Nation” on CBS.

Antony J. Blinken, Mr. Obama’s deputy national security adviser, was booked late Friday onto Sunday talk shows to defend the president’s approach. Mr. Blinken said existing sanctions were having an impact on the Russian economy. “All of this is creating a dynamic in which what Putin has promised to his people, which is growth and prosperity, cannot be delivered,” he said on CNN’s “State of the Union.”

The administration also signaled that even if Russia backed down in eastern Ukraine, the United States would not lift sanctions as long as it controlled Crimea. “Sanctions imposed because of its actions in Crimea will remain so long as those actions continue,” Tom Malinowski, the assistant secretary of state for human rights, wrote on the department’s blog.