Gasoline prices are pushing even farther above $4 a gallon, the highest price that American motorists have faced since July 2008, as calls grow to ban imports of Russian oil.

Prices at the pump were rising long before Russia invaded Ukraine and have spiraled faster since the start of the war. The U.S. national average for a gallon of gasoline has soared 45 cents a gallon in the past week and topped $4.06 on Monday, according to auto club AAA.

"I am looking at the possibility of walking to work," said Asiya Joseph, who had just paid $4.29 a gallon at a BP station in Brooklyn, New York. "This is...