Republicans and Democrats in Congress are pushing President Biden to ban Russian energy imports as they search for new ways to punish Moscow for its bloody invasion of Ukraine, even as the White House resists the idea, which it argues would drive up the price of gasoline and other energy costs for Americans.

The effort reflects a furious, bipartisan backlash on Capitol Hill to President Vladimir V. Putin of Russia and his unprovoked offensive in Ukraine, an attack that has left thousands dead and sent 1 million Ukrainians fleeing from their country in just a week.

The growing momentum behind the effort, which experts have said would be largely symbolic, also underscored how few tools both Congress and the White House have at their disposal as they grasp for new ways to weaken Mr. Putin.

Russian energy represents a small fraction of American imports, and Moscow is already having trouble exporting its oil even in the absence of sanctions, as traders, insurance companies and refiners slash purchases of Russian crude for reasons ranging from reputational risk to the safety of tankers in a war zone.