Google commands more than 90 per cent of the market in countries including Germany and is broadening its services to areas such as self-driving cars, thermostats and Web infrastructure.
The expansion is prompting calls by publishers, phone companies, politicians and data-protection officials in Europe to rein in the company's reach.
YouTube, a Google unit, threatened on Tuesday to block music videos from independent labels that haven't agreed to be part of a planned subscription service.
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Google's critics include German Economy Minister Sigmar Gabriel, a Social Democrat who is deputy chancellor. Germany "must seriously consider" threatening to dismantle "companies like Google" with antitrust laws, he said in an op-ed in May.
Google faces particular concern in Germany, where spying under the Nazi and communist police states still resonates. In one response, Google agreed in 2010 to blur images of German buildings in its Street View application if residents objected.
De Maiziere said he prefers the threat of antitrust fines and EU privacy rules. Companies like Google should be told that "if you offer services in the European Union, you have to observe European rules," he said.
European governments and US technology companies "are more like allies" in seeking to keep intelligence agencies from siphoning off data because the companies worry about losing business in Europe and Asia, de Maiziere said.
The German government plans to host a meeting with US Internet companies in Berlin on June 27 to discuss data protection in the wake of Snowden's revelations of global NSA surveillance.
As German prosecutors and lawmakers investigate allegations that the NSA eavesdropped on Merkel's phone, Snowden can't expect free passage to testify, said de Maiziere, who is the cabinet member responsible for data privacy and federal law enforcement.
"We have an extradition treaty with the US and we fulfill treaties," he said. "We would start extradition proceedings," though Snowden would have legal recourse and "it wouldn't be a simple procedure."
No government leader's phone can be as secure as "a one-to-one conversation in a park," de Maiziere said. "Every government official must know that. A mobile phone will never be totally secure."
EU-US talks on a data-privacy agreement, which began in 2011, are complex and will take time, he said.
"I don't expect quick progress," he said. "We'll get one at some point."
- Bloomberg