Speaking to ITV News he said: "I think we've got to take really effective steps now, I would want a rule change to say in clear cases of anti-Semitism there ought to be automatic expulsion."
He added: "We've got to be much stronger in saying denying the problem, is part of the problem."
Lord Triesman, a former Labour general secretary and foreign office minister, said the party and its leadership are “institutionally anti-Semitic”, while Lord Darzi and Lord Turnberg also quit the Labour whip.
Sir Keir said their decision “reinforces the sense of duty that we have to do whatever is necessary in the Labour Party to make sure that people like David (Lord Triesman) … feel that they can return to the Labour Party with confidence”.
The shadow Brexit secretary said it was “very easy for people in leadership positions” in the shadow Cabinet to “duck responsibility”.
He told BBC Radio 4’s Today programme: “I think we have got to take decisive action.
"Firstly, I would support a rule change that says you expel in clear cases of anti-Semitism automatically, just as we do for people who support another political party an election.
“Secondly, be very clear if you deny we’ve got a problem, that’s part of the problem.
“Thirdly – and this is a cultural and attitude issue – now the Equality and Human Rights Commission is looking at the Labour Party, we should throw open the books and say ‘you’ve got access to anything, you have got access to any member of staff, we have made some process changes which have improved things but we have still got a problem, help us through this’.
“Many organisations circle the wagons when they are challenged. That is the wrong approach, we have got to be very, very open.”