The European Commission warned Google on Monday that the company might have abused its dominant position in online searches, but it gave Google a chance to settle an antitrust investigation without facing formal charges.

------Before sending a letter formally outlining the offer on Monday, Mr. Almunia told Eric Schmidt, the executive chairman of Google, by telephone last week that the company should respond “in a matter of weeks” to avoid the charges, which are known as a Statement of Objections.

Antitrust fines in Europe can reach up to 10 percent of a company’s annual global revenue. Google’s revenue was nearly $38 billion last year.