EU Competition Commissioner Joaquin Almunia has given Google until "early July" to outline how it proposes to tackle antitrust concerns.
An 18-month investigation by the EU suggested that Google favours some of its own services over rivals in search results and related services.
"I want to give the company the opportunity to offer remedy proposals that would avoid lengthy proceedings," said Almunia. "By early July, I expect to receive from Google concrete signs of their willingness to explore this route."
Google has repeatedly denied that it is in violation of Europe's antitrust rules.
In May, Google's execuctive chairman Eric Schmidt said he would co-operate fully with the Commission to understand its concerns, but said Google needed specific examples of where and how it has broken the law.
“We’re not aware we’ve done anything wrong, but we’re happy to be educated to the contrary," said Schmidt. "As far as we can tell, the way we’ve designed Google is pro-competitive and positive for end users. If it’s not then we want to hear why. We want the details,” he said.
Almunia has warned that if Google's proposals are not satisfactory, then the European Commission would institute formal proceedings against the search giant.
"I strongly believe that users and competitors would greatly benefit from a quick resolution of the case," he said.
"It is always better to restore competition swiftly in fast-moving markets, provided of course that the companies concerned are ready to seriously address and solve the problems at stake."