But the Labour leader’s aides later backtracked to say the position could change if Nicola Sturgeon’s party wins control of Holyrood in the 2021 Scottish Parliament election.
Mr Corbyn kicked off a two-day tour of Scotland in Glasgow on Tuesday aiming to help his party retake some of the seats it lost to the SNP landslide in the 2015 general election.
The Labour leader was heckled as he visited a community centre in Glasgow.
He was approached by a Church of Scotland minister who branded him a "terrorist sympathiser."
Mr Corbyn was showing off a tartan scarf gifted to him by a charity, when Scotstoun Parish Church’s Reverend Richard Cameron asked why he wasn't wearing an "Islamic Jihad scarf".
Rev Cameron told the Labour leader: "Do you think the man that's going to be prime minister of this country should be a terrorist sympathiser, Mr Corbyn.
"Who's going to be the first terrorists invited to the House of Commons when you're prime minister?"
Mr Corbyn did not react to the criticism, which was apparently made over his willingness to talk to groups such as Hamas and the IRA as part of peace processes.
In response, Rev Cameron said: "Aye, he's running away."
The minister was later rebuked by the Church of Scotland.
Rev Cameron has been criticised in the past for his allegedly homophobic and racist comments, in particular against gay priests.
ITV News Political Correspondent Libby Weiner on the latest from Corbyn's campaign trail
In the 2017 election, Labour made a slight recovery, compared to the 2015 poll, but the SNP still had 35 of the 59 Scottish constituencies in the last parliament.
In an interview likely to rile Ms Sturgeon, Mr Corbyn said: “No referendum in the first term for a Labour government because I think we need to concentrate completely in investment across Scotland.”
But pressed on whether it would be undemocratic to deny the referendum if the SNP again won the majority of Scottish seats in the December 12 vote, the Labour leader said: “If the SNP win the majority of seats that’s the election of those MPs.
“I’m very clear that a Labour government’s priority is investment in Scotland.”
Labour advisers later dialled back on Mr Corbyn’s statement to make it clear that the party’s position could change if the SNP wins the 2021 Holyrood election.
The SNP seized on the comments, accusing Mr Corbyn of taking the “undemocratic position of simply ignoring the Scottish people” and warning him over asking for support to form a government.
Social justice spokesman Neil Gray said: “With the once-dominant Scottish Labour Party now at the point of extinction, and Labour voters turning to the SNP, Jeremy Corbyn is in absolutely no position to tell the people of Scotland if and when they can have a say over their own future.
“As we have made crystal clear, no one looking for support from the SNP after this election should bother to even pick up the phone unless they are prepared to accept the democratically expressed will of Scotland.”
Elsewhere, Labour pledged to outspend the Tories by investing an additional £26 billion in the NHS to rebuild “crumbling” hospitals and improve patient care.
Shadow chancellor John McDonnell, in London, said his party was offering an annual average 4.3% real-terms increase in health spending over the next four years.
While the spending pledge was widely welcomed by health groups, Tory Health Secretary Matt Hancock claimed Labour’s plan for a four-day week would cost the NHS a fortune.
In Glasgow, during his first speech of his Scottish tour, Mr Corbyn tried to dissuade voters from backing the SNP by stressing only Labour or the Tories could form a UK government.
“Nobody else can form a government,” he told supporters at the Heart of Scotstoun community centre.
He reiterated his pledge to invest more than £70 billion in Scotland as part of his “green industrial revolution” to boost jobs while tackling the climate crisis.