Barry Sheerman described the contest to replace Ed Miliband as being in “meltdown” as a result of the offer to give non-members a vote in return for paying £3.
Many in the party believe the mechanism is being used for different reasons by both Conservative supporters and those from the hard left to skew the leadership contest in Mr Corbyn’s favour.
Mr Sheerman wrote on Twitter: “Labour Party leadership campaign is in meltdown as our traditional enemies sign up & take over our Party! NEC should suspend election now!”
He said that Labour had spent years defending itself from “entryism” but “we have handed our Party to them on a plate! Stop this madness now!”
Mr Corbyn’s apparent popularity has caused alarm in sections of the party fearing his success in the leadership race would make Labour unelectable.
But concern about the conduct of the race has been tempered by a desire to see Labour getting back on the front foot after its election defeat and avoid a repeat of the party’s muddled response to the Government welfare reforms before the summer break.
Halifax MP Holly Lynch said: “The Labour party needs to be an effective opposition more than ever - both in Westminster and in our streets - and I believe that suspending or delaying the leadership election would only undermine our ability to do that.
“Although the Labour party had the right intentions when it sought to give more people a say in the election, we must ensure that robust procedures go with it to weed out those seeking to vote for all the wrong reasons.
“The Labour party is a broad church which is good for debate, but I strongly believe that we need a leader who offers a bright future for the party and the country, and is able to take the whole party forward. For me, that is Andy Burnham.”
A spokeswoman for Yvette Cooper’s leadership campaign said the Normanton, Pontefract and Castleford MP said it was up to the party to ensure the contest is a “fair process”.
In his latest bid for support, Mr Corbyn has hinted that under his leadership the party might reverse Tony Blair’s scrapping of its constitutional commitment to state ownership.
Mr Blair’s success in removing the old “Clause IV” was seen as a key moment in the New Labour project leading up to its 1997 landslide but Mr Corbyn has called for the party to be more positive about state intervention.
He told The Independent on Sunday: “I think we should talk about what the objectives of the party are, whether that’s restoring the Clause IV as it was originally written or it’s a different one, but I think we shouldn’t shy away from public participation, public investment in industry and public control of the railways.
“I’m interested in the idea that we have a more inclusive, clearer set of objectives. I would want us to have a set of objectives which does include public ownership of some necessary things such as rail.”
Liz Kendall, who is viewed as the Blairite candidate in the leadership contest, said: “This shows there is nothing new about Jeremy Corbyn’s politics. It is just Bennism reheated, a throwback to the past, not the change we need for our party or our country.”