The Labour leader said he would continue to campaign in marginal seats across the United Kingdom while opposing Theresa May's government in Westminster.
Some senior figures within the Scottish party - including leader Kezia Dugdale and Edinburgh South MP Ian Murray - had openly criticised Mr Corbyn's leadership ahead of the election.
Mr Corbyn was greeted with cheers and a long standing ovation as he arrived at the first meeting of the Parliamentary Labour Party since the Conservatives lost their Commons majority, in marked contrast to the hard meetings he had with his critics in the party prior to the election.
"We will continue to take the fight to the Tories and I will be out campaigning around the country in Conservative marginals in those extra seats we need to gain to deliver the government for the many that nearly 13 million people voted for last week", he said.
Rutherglen and Hamilton West, the first result announced in Scotland, was a Labour gain, with the party also picking up a seat in its one-time heartland of Glasgow, where it suffered humiliating defeat two years ago.
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Jeremy Corbyn has used perhaps the most infamous of soundbites from the General Election campaign against the very person who said it.
"We will continue to take the fight to the Tories and I will be out campaigning around the country in Conservative marginals in those extra seats we need to gain to deliver the government for the many that nearly 13 million people voted for last week".
"Far from being strong and stable, the Government Theresa May is putting together is weak, wobbly and out of control".
Theresa May has no mandate to govern, he suggested, and her administration is "on notice from voters".
"We are now a government in waiting and we must think and act at all times with that in mind". "That is our responsibility to the huge numbers who voted for our manifesto last week".
The source added that some of Mr Corbyn's critics in Parliament were "gracious enough to point out that they hadn't always had confidence in his leadership but they did now and that they had underestimated him".
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