Ian Murray said the power struggle over new rules could lead to the Scottish party “shutting down”.
The former shadow Scottish secretary added it was “utterly critical” that reforms - which the party leader’s supporters fear swings the balance against him on the ruling National Executive Committee (NEC) - are backed on the conference floor on Tuesday.
At a Labour fringe meeting, he said the “branch office” tag that the party has in Scotland had “completely destroyed” it.
“If certain people on the National Executive Committee run a campaign to vote these rules down tomorrow they are in danger of not just not helping the Scottish Labour party, they are in danger of shutting the Scottish Labour party down,” he said.
Mr Corbyn earlier lost the latest battle in the struggle over rule changes in the party, including appointments to Labour’s ruling body.
A fresh attempt by the leader’s allies to stop the party’s Scottish and Welsh leaders or their representatives sitting on the NEC was rejected when it met on Monday morning.
It followed a “powerful address” by Welsh leader Carwyn Jones urging the committee not to let Wales down.
The First Minister is understood to have told the NEC that the party in Wales is the most successful part of the Labour family but nationalists mock it as a “branch” office.
He is said to have told NEC members that the measures were needed to counter those claims as he urged them not to “water down” the package of reforms.
The NEC knocked back the bid to delay the changes without a vote, with members being told the issue had been backed twice at previous meetings.
But proposals will go before the wider party through a vote on the conference floor on Tuesday.
Mr Murray said Labour lost in 2015 because David Cameron set Scottish nationalism against English nationalism.
“That’s what all the analysis has told us,” he said.
“The reason that a lot of members of the Labour party and Labour supporters don’t know that analysis is because the party has been refusing to release it.”
He added: “We are a broad church of a party and we always have been and I will not be leaving the Labour party.”
Scottish Labour leader Kezia Dugdale told BBC Scotland: “Exactly what we agreed yesterday is exactly what is happening tomorrow in a vote on the conference floor.
“We have been working on these proposals for a long time. It is the right thing for Scotland and the right thing for the whole party and I am looking forward to the debate tomorrow.
“The proposals are very clear that the position on the NEC is for the leader of the Scottish and Welsh parties to either take themselves or to nominate, just as Jeremy Corbyn nominates the people that sit on the shadow cabinet that sit in the NEC.”
A separate attempt to thwart the reforms was also rejected on the floor of the conference hall.
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