"If you are anti-Semitic you shouldn't be in the Labour Party", he said.
The leadership hopeful will be launching his campaign today in Manchester.
Sir Keir said that he had argued within the party for tougher action, with automatic expulsion for anyone found to be anti-Semitic.
Ms Siddiq said: "When I made the hard decision regarding who I would nominate, in my mind I kept thinking who I would want standing at he dispatch box in the House of Commons, taking on Boris Johnson in a forensic, detailed manner - who will hold this government to account".
However shadow foreign secretary Emily Thornberry, with 10 nominations, and Clive Lewis, with just four, appear to be struggling.
Candidates who reach the magic number of 22 - 10% of Labor MPs and MEPs in the PLP, who are a total of 212 - must then secure the support of 5% of the constituency's Labor branches or at least three constituents, two of which must be composed of unions.
Shadow Business Secretary Rebecca Long-Bailey, Lisa Nandy and Jess Phillips all secured the 22 supporters needed to continue the competition. "It seemed to me that if you have been chucked out of the Labour party for supporting another political party, you should be chucked out for being antisemitic", he said.
The deadline for securing enough nominations is 2:30pm on Monday, otherwise candidates will be forced to drop out.
Such a move could damage support for Ms Long-Bailey who has tried to position herself as the standard bearer for the left.
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Sir Keir would not be drawn into personal criticism of Mr Corbyn, although he said that it was right that he was now stepping down after Labour's "devastating" general election defeat.
His vow to "retain our radicalism" is a signal he'd retain some of the outgoing leader's platform, while at the same time making a vow "to rebuild people's trust in Labour as a force for good and real change".
"Losing an election is probably the most important thing you can measure a leader against, and obviously we lost very, very badly", she told Sky News.
"I am not going to get into ranking Jeremy Corbyn out of 10".
"On that basis I would give him, on that, nought out of 10". He is a friend and a colleague.
"I do believe that we can be an effective opposition, that we can take the challenge to Boris Johnson, that we can restore trust in our party", he added.
"It gives us the best possible mandate to stand up for the members that the Labor Party can bring together to give our country the radical, dynamic, compassionate Labor government that the country deserves".
Over the weekend, the left-wing activist group Momentum, which helped propel Mr Corbyn to the leadership in 2015, said it was recommending support for Ms Long-Bailey and Ms Rayner. "Frankly, I find all the labels just get in the way", he said.