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LONDON — One of Europe’s top policy makers on Tuesday called on Google to offer more concessions in a long-standing antitrust investigation that the search giant is facing in the European Union.

Google has been embroiled in a four-year inquiry into its dominant position in Europe’s search market, and some European politicians backed a nonbinding vote last year to break up the American technology giant.

The company is also under growing scrutiny over how it pays taxes across the region, and a recent privacy ruling by Europe’s highest court gave people the right to request that links about themselves be removed from Google’s search results.

Speaking at a conference in Munich, Günther Oettinger, the European Union’s commissioner for the digital economy, said that while he respected what Google’s founders had achieved, the company must honor European rules about its operations in the 28-member bloc.

“Google has to bring more offers to us,” Mr. Oettinger said when questioned about Europe’s continuing antitrust investigation. “Google must be ready for a convincing compromise.”

Mr. Oettinger said that the European Commission wanted to find a resolution to the lengthy Google antitrust case by mid-2015. His colleague, Margrethe Vestager, the new competition commissioner, is leading the case.

Last month, Europe’s competition authorities sent questionnaires to companies in areas like online mapping and travel, as part of a renewed effort to determine whether Google favors its own services over those of competitors. The company holds a roughly 90 percent share of the European online search market.

“A search platform needs to be objective and neutral,” Mr. Oettinger told the audience in Munich. “Google has to accept our European rules.”

And in a sign that Google’s problems in Europe may be growing, Mr. Oettinger said he would invite the search company to discuss changes to European copyright rules.

Several European publishers, including Axel Springer of Germany, have criticized Google’s perceived dominance over how individuals find content online. And some countries have adopted copyright laws demanding that online news aggregators like Google News pay to show publishers’ content on their websites.

In Spain, Google shut down its news aggregation service last month after the country’s lawmakers passed rules that forced the company and other news aggregators to pay Spanish publishers for the use of their content.

European policy makers are contemplating overhauls of copyright rules, which might expand them across the Continent, though Google and other Internet companies are adamantly opposed to the changes.

Asked whether Europe was taking an antagonistic stance toward American tech companies, Mr. Oettinger tried to take a conciliatory tone. “It’s not a battle,” he said. “But a competition and cooperation.”