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In an email sent on Friday morning, Corbyn said he was “sorry” that the party failed to make it into power during his almost five years in charge.
But he defended Labour under his leadership as having “changed the agenda on austerity and how the economy is run”.
Corbyn also repeated the promise, made during his final prime minister’s questions last month, not to step back from politics once he is replaced as leader on Saturday.
“I’ll be out there campaigning for socialism,” he said. “I can assure you my voice will not be stilled.”
Keir Starmer, the shadow Brexit secretary, is widely expected to win the race to replace Corbyn.
Left-wing allies of the outgoing leader had urged members to vote for Rebecca Long-Bailey, but the shadow business secretary’s campaign had a slow start.
The coronavirus pandemic also effectively froze the leadership campaigns of Starmer, Long-Bailey and Lisa Nandy.
The announcement of Corbyn’s successor will be made on Saturday morning by email.
Plans to hold a special conference in central London to reveal the result were shelved as a result of the coronavirus outbreak.
In his message, Corbyn said: “Over the past five years we have changed the agenda on austerity and how the economy is run.
“In 2015, opposing austerity was seen as radical; today it is the political mainstream.
“A majority of the public supports Labour on issues such as public ownership and higher taxes on the richest.
“We now look forward as a party of economic inclusion, climate justice, peace and human rights.”
He added: “Of course, we could have achieved so much in government, and I am sorry that under my leadership we did not get there.
“In 2017 we came close, winning the biggest increase in the popular vote since 1945.
“Sadly, the 2019 election was a Brexit election and our attempt to bridge the gap between Leave and Remain voters was unsuccessful.”
Corbyn told members: “Together we have the ideas, policies, energy and organisation to win a Labour government next time.”
“I will continue to campaign on the issues and principles that have motivated me as leader, as an MP, as a councillor and as a party member for more than 50 years,” he said.
“I can assure you my voice will not be stilled. I’ll be out there campaigning for socialism, peace and justice, and I feel sure we’ll be doing that together.”