Google asked a judge in its home state of California to invalidate a non-complete agreement that is at the heart of Microsoft’s lawsuit against Google and its former employee Kai-Fu Lee, which Microsoft filed last week.

Google said last week it had tapped Lee to head up the company’s first R&D center in China, which is slated to open during the third quarter.

Google’s lawsuit alleged that the non-compete provision that Lee agreed to in an earlier Microsoft agreement was overreaching and unlawful, according to reports.

Lee joined Microsoft in 1988 to establish an R&D center in Beijing. He later moved to Microsoft’s Washington-based headquarters as VP of its interactive computer technologies, which included speech recognition.

The legal spat comes at a time when Microsoft is stepping up its efforts to rival Google’s dominant position in the search market.