The departures come after Google’s decision last year to hire John Krafcik, the former president and chief executive of Hyundai America, to be chief of the car project, as part of a plan to spin the effort out as a stand-alone company under the Alphabet umbrella.

The X research group, often called Google’s “moonshot” division, is under increasing pressure to show that at some point the company can expect a financial windfall from its projects. Google’s self-driving car project has been a pioneer in autonomous vehicle technology, but a commercial version of the car is still likely to be several years away.

Mr. Urmson has been unhappy with the direction of the car project under Mr. Krafcik’s leadership and quarreled privately several months ago with Larry Page over where it was headed, according to two former Google employees. A spokesman for Google declined to comment on those discussions, but Mr. Urmson disputed they were a reason for his departure.

After the dispute, Mr. Urmson decided to take the summer off and only recently decided to leave the company. He told members of the self-driving car team about his decision on Thursday, the former employees said.

In a post published on Medium Friday afternoon, Mr. Urmson said he had not decided what he will do next. “If I can find another project that turns into an obsession and becomes something more, I will consider myself twice lucky,” he wrote. “I have every confidence that the mission is in capable hands.”