Microsoft Corp. unveiled new partnerships with politically connected Chinese companies in an effort to open doors to more sensitive and official business in the vast China technology market.

The deals—which include a tie-up with a state-owned Chinese military-technology consortium—were disclosed on Wednesday, the same day Microsoft Chief Executive Satya Nadella joined other U.S. business leaders in meeting with Chinese President Xi Jinping in Seattle. They come as Microsoft seeks to make inroads into the world’s second-largest...