BRUSSELS — Google has struggled for years to settle an antitrust investigation in the European Union, to avoid a huge fine and the stigma that would come with breaking the law.

Now it appears there may be no end in sight to the Internet search giant’s antitrust problems in Europe even if it does finalize a tentative accord reached in that case, according to a letter from Joaquín Almunia, the competition commissioner and the most powerful antitrust enforcer in the 28-country bloc.

Mr. Almunia has not given up on reaching a final settlement with Google in the case, in which the American company is accused of abusing its dominance in the online search and adverting business. But the letter, made available by a person who did not want to be identified because the document had not been made public, indicates that Mr. Almunia is trying to marshal support for an unpopular provisional deal by emphasizing to critics that new investigations await Google.

In the letter, written June 11 to his commission colleagues, Mr. Almunia said that the European Commission was prepared to investigate “many allegations, the various practices that they cover, and the new types of markets that are affected.” He mentioned social networks, streaming, cellphone operating systems and mobile apps as areas that could face scrutiny.