The Labour leader did say he would be inclined to block such a vote until after the Brexit negotiations are complete, but his admission that he would “consider” a referendum was seized upon by other pro-union parties yesterday.
It came as Mr Corbyn ruled out the prospect of forming a government in a “progressive alliance” with the SNP as polls indicate that Labour is closing the gap to the Tories.
Nicola Sturgeon had indicated at the weekend that she would prefer to see the Labour leader in power rather than Theresa May.
Mr Corbyn was briefing journalists yesterday morning after attending a rally in front of hundreds of supporters in Glasgow on Sunday night
Asked about the recent vote in the Scottish Parliament for a second referendum, Mr Corbyn said: “I’ll obviously open discussions with the Government in Scotland and listen very carefully to what the Scottish Parliament says.
“I would ask them to think very carefully about it and suggest it would be much better to have this question dealt with at the conclusion of what are very serious and very important Brexit negotiations.”
Mr Corbyn said the appetite for a second referendum is “declining very fast”.
He added: “Obviously I realise the Scottish Parliament has made a decision of its view.
“I will receive and consider that, but I think the priority has to be the Brexit negotiations and dealing with that first.
Asked whether he would endorse a referendum after the Brexit negotiations are complete, he added: “Let’s look at the issue at that point.”
The comments were seized upon by Scottish Conservative leader Ruth Davidson.
“Nicola Sturgeon has said she’d put Jeremy Corbyn into Number 10. Now Jeremy Corbyn says he is happy to ‘open discussions’ with her about a second referendum,” Ms Davidson said.
“Labour voters in Scotland now know that Jeremy Corbyn would sell them down the river.
“I will never fold against Nicola Sturgeon’s demand for a second referendum.
“It is clearer than ever that only by voting Scottish Conservatives on 8 June can we send her a message to take if off the table.”
A spokesman for Mr Corbyn last night sought to play down the comments insisting that the “discussions” were a reference to all Scottish issues.
He added: “Jeremy Corbyn and Scottish Labour have repeatedly said that a second independence referendum is both unwanted and unnecessary. Labour firmly opposes a second independence referendum.”
Mr Corbyn, who has already ruled out any agreement with the SNP, spoke out on the issue again yesterday.
He said: “There will be no deals. There will be no alliance. We’re fighting this election to win.
“Only Labour or the Tories can win this election and voting Labour is the only way to remove Theresa May from office and build a Scotland for the many not the few.” His comments follow an interview with the BBC in which Ms Sturgeon said Mr Corbyn was not “credible as an alternative prime minister”.
But the SNP leader also said that “if there was to be a hung parliament of course we would look to be part of a progressive alliance that pursued progressive policies”.
Recent opinion polls across the UK have showed Theresa May’s lead over Labour shrinking.
A poll by Survation for ITV’s Good Morning Britain (GMB) today puts Labour on 37 per cent, up three points on a week ago and six points behind the Tories who are unchanged on 43 per cent.