Labour will appeal against a High Court ruling which said new party members should have the right to vote in its leadership election.
Judges ruled in favour of five supporters who accused the party's National Executive Committee (NEC) of unlawfully "freezing" them out, even though they had "paid their dues", when it decided that full members would not be able to vote unless they had six months' continuous membership up to July 12.
Party officials said Labour would mount a legal challenge to "defend the NEC's right" to uphold its rules.
The leadership race was plunged into chaos by the court ruling and members of Labour's procedures committee discussed how to respond in a hastily arranged conference call.
Labour was given permission to go to the Court of Appeal but Jeremy Corbyn's allies had urged the party not to pursue the option, claiming members' money was being squandered on stopping them from voting.
Conservative Party chairman Sir Patrick McLoughlin said: "This summer, the Labour Party have held more High Court battles than leadership hustings.
"At a time when the people of Britain look to a party who will fight for them and their family, Labour are spending their summer fighting amongst themselves."
A change.org petition has been set up by the four Labour members who won the court case titled: 'Labour Party: Don't Appeal the Court Decision!'
It reads: "When we joined the Labour Party, we were told we would be able to vote in any leadership election.
"After Labour's National Executive Committee ruled that we weren't allowed to vote, we took the decision to challenge its decision in court. We crowdfunded our legal costs and the High Court has now recognised our right to vote.
"However, we understand the Labour Party are considering appealing this decision. If they do so, they will be spending Labour Party members' money on trying to stop members from voting, money that could be much better spent on defeating the Tories.
"We are urging the Labour Party to respect democracy and not waste members' money on trying to prevent a quarter of its membership from voting."
The petition has almost 6,000 supporters so far.