BRUSSELS — Lawmakers here have introduced a measure in the European Parliament that could require American companies like Google and Yahoo to seek clearance from European officials before complying with United States warrants seeking private data.

The measure, an amendment to a broader electronic privacy law pending in Parliament, is a response to Prism, the secret spying program led by the National Security Agency that came to light in June. Europeans were outraged by the revelations that some of the biggest American Internet companies, many of whose users live in Europe, were required by the United States authorities to share information in e-mail, Web searches and other online data.

Parliament’s Committee on Civil Liberties, Justice and Home Affairs may vote on the amendment as soon as Monday, said Jan Philipp Albrecht, the German member who is responsible for steering the legislation through the Parliament. His office later clarified that the vote could be delayed until Thursday. Once it wins approval by the committee, Mr. Albrecht may begin negotiations on the Parliament’s behalf with European governments, which are discussing their own version of new privacy rules.

But a European Union official, who spoke on condition of anonymity, said the vote could be further delayed if the United States intervened or if there was heavy lobbying by tech industry groups that oppose the bill.