Sir Stephen has come under pressure to quit after the deaths of John Yuill and Lamara Bell in a car crash on the M9.
The incident was reported to the police but they failed to follow it up for 72 hours.
An independent investigation into the incident is now taking place and a review of all police call handling has been ordered by the Justice Secretary.
Labour’s justice spokesman Hugh Henry has tabled the motion, stating that the public are “rapidly losing confidence in Police Scotland after a series of major mistakes”.
Mr Henry said: “Revelations of recent days appear to confirm that the tragedy on the M9 wasn’t an isolated incident and was the result of a number of failures since the creation of Police Scotland.
“Sir Stephen House should resign with immediate effect.
“Only when the chief constable moves on can the Scottish Government fully investigate the failings in Police Scotland and get a grip on policing across our country.
“There are also serious concerns about accountability. The Scottish Police Authority has utterly failed to hold Police Scotland to account in any way.
“This isn’t an issue of party politics - it’s about the policing of our country. I hope members from all the different political parties can support this motion.”
It is the latest in a series of controversies to hit Police Scotland and Sir Stephen’s leadership.
Sir Stephen said last week that he believes it is right for him to stay and provide leadership within the organisation.
He said: “In anything like this I consider my position. I think you would be inhuman if you didn’t. You see what’s happened over the last week and think about that, and I certainly have.
“I believe the right thing to do is to stay to get through this process, to get through this tragic event and the series of events that followed it, and to see what can be done to fix the situation.
“I don’t want anyone out there thinking I’m the type of person that says ‘I’ll never go, I’ll have to be forced out’.”