Prohibition on Imports of Russian Oil Act This bill requires the President to prohibit the importation of petroleum products from Russia. Petroleum product means crude oil, residual fuel oil, or any refined petroleum product, including natural gas liquid product. Further, the bill authorizes the President to (1) modify or remove the prohibition for some or all petroleum products if the President notifies Congress that such modification or removal is appropriate given the situation in Ukraine, and (2) use appropriate authorities to impose civil or criminal penalties as necessary to enforce the prohibition.