The 24-year-old, who was due to become a father, was shot dead by a firearms officer in Streatham Hill, south London, last Monday night.
The Independent Office for Police Conduct (IOPC) has since launched a homicide investigation into his death, but the Met is yet to confirm if any of the officers involved have been disciplined.
Two south London MPs have now joined calls from campaigners and Mr Kaba’s family in calling for the officer to be suspended.
Bell Ribeiro-Addy, MP for Streatham Bell, and Harriet Harman, MP for Camberwell and Peckham, have both signed a letter calling it “incomprehensible” that the officer has not been disciplined.
The letter reads: “This is a matter which could not be more serious. A young man has lost his life and our sympathies are with his parents and his family. It is incomprehensible that the officer who killed Chris Kaba is not suspended.
“The family, the local community, and we as MPs want to see a swift response in recognition of the utmost seriousness of this. Chris’ death was on Monday, it is now Sunday and the officer has yet to be suspended.
“We are calling on the Met to suspend the officer today. Even moving him out of firearms duties or into back-room duties would not be sufficient in view of the seriousness of this matter. It must be suspension and it must be now.”
MP Dawn Butler, who represents Brent Central, also condemned the shooting. She wrote on Twitter: “I was at this meeting and I very much supported the call to suspend the officer responsible. The Met is already in special measures and this slow response to something as serious as this is just totally unacceptable. No confidence. No justice. No peace.”
It comes after hundreds of protesters marched through Whitehall on Saturday demanding justice for Mr Kaba.
Members of his family were joined by supporters bearing placards proclaiming “justice for Chris Kaba”, “abolish the Met” and “no justice, no peace”.
Protesters gathered in Parliament Square from midday before marching along Whitehall and then on to Scotland Yard.
Mr Kaba was driving an Audi that was rammed and boxed in by police on Monday night. He was killed by a single shot fired through the driver’s side of the car’s windscreen.
His family has called for the officer who fired the shot to face suspension. In a statement released before the demonstration, Mr Kaba’s family asked the police watchdog to conclude its investigation within “weeks or months, not years”.
It added that restoring public confidence in the justice system required the IOPC to make decisions on “a timescale that delivers justice to all concerned”.