Seznam, which attracts as much advertising spend as Google in the Czech Republic, took its grievance to the European Commission nearly three years ago.
It subsequently joined lobbying group FairSearch whose complaint triggered the European Commission's investigation into Google's mobile operating system Android which ultimately led to a record 4.34 billion euro ($4.9 billion) fine.
"Time is running out, every day makes a difference. Seznam is losing market share because of Google's search engine installed by default on mobiles," said Michal Feix, Seznam's former chief executive and now a partner at a consultancy advising the company.
EU antitrust enforcers said Google, a unit of Alphabet Inc., had used its Android market power to hinder rivals.
Google' senior vice-president of global affairs, Kent Walker, said in a blog this week that his company planned to prompt users to choose their preferred browsers and search apps, but he did not provide details.
Feix welcomed that idea in principle. "It is probably the solution we are looking at but it depends on the details. Walker's blog lacked details," he said.
Google spokesman Al Verney declined to comment.
(Reporting by Foo Yun Chee; Editing by Edmund Blair)
By Foo Yun Chee