Jeremy Corbyn has poured cold water on the idea that Labour could support an attempt to attach a referendum to Boris Johnson’s Brexit deal at next Saturday’s emergency sitting of parliament.

The prime minister is expected to convene the House of Commons for a rare Saturday session, either to ask for support for his deal, if he succeeds in striking one at this week’s European council – or to request that MPs back a no-deal exit at the end of this month.

Pro-remain MPs hope to amend any motion put by the government, to insist that Johnson’s deal be subject to a public vote.

But asked by Sophy Ridge on Sky News whether some MPs would be more likely to support a deal if it would be put to a referendum, Corbyn said, “I think many in parliament, not necessarily Labour MPs but others, might be inclined to support it, because they don’t really agree with the deal – but I would caution them on this.”

He said he would instead be keen to see a Labour-style Brexit deal, including a customs union, and guarantees on workers’ rights and environmental standards, put to the public.

Corbyn’s comments appeared to put him at odds with the shadow Brexit secretary, Keir Starmer, who said in a speech in Glasgow on Saturday that Labour would press for any deal Johnson secures to be subject to a referendum.

“Next week our priorities are clear: if Boris Johnson does manage to negotiate a deal, then we will insist that it is put back to the people in a confirmatory vote,” Starmer said.

The Labour leadership has been torn for many months between what it sees as the need to reach out to leave voters in Labour constituencies and the party’s membership, which is strongly remain.

The shadow chancellor, John McDonnell, has been accused by some on the left of the party in recent days of making too many concessions to the People’s Vote campaign.

The shadow business secretary, Rebecca Long-Bailey, who is a close ally of McDonnell’s and widely regarded as a potential future leadership contender, struck a different tone to Corbyn on Sunday.

She said Labour’s policy was that any deal should be put to the public, whether negotiated by a future Labour government, or by Johnson. “I think it should be the position if we’re faced with a deal that’s passed through the Commons by an unelected Tory prime minister that could potentially be damaging to our economy,” said Long-Bailey.

On Sky, Corbyn also declined to offer support to those Labour MPs who wanted a referendum held before any general election.

Asked which should come first, he carefully laid out Labour’s position, as agreed at the party’s conference in Brighton last month.

“We have to get a deal that we can agree on if possible, and the Labour position is that we would take this to a public vote, with a Labour government. Within three months we would hope to reach agreement with the EU. We believe that to be possible, along the lines we’ve set out – and within six months, hold a referendum,” Corbyn said.

“And a Labour government would then implement the results of that referendum: between a sensible relationship with Europe, and remain.”

Asked when an election should be, Corbyn said: “We’ll look at any deal that comes up, before we trigger an election.” He said he was keen to focus on other issues, including investment, tackling the climate crisis and education.

He also brushed aside the question of whether he would step down if Labour lost another general election, as McDonnell suggested he would in an interview with GQ magazine on Friday.

“We’re not expecting to lose the next election: it’s a hypothetical question, and it’s up to the members of our party to decide who the leader is,” Corbyn said. Asked to identify potential candidates, he said: “I am not into the business of ordaining people.”

Asked what Labour will do if Johnson failed to pass a deal and refused to implement the Benn act by not requesting a delay to Brexit, Corbyn said his party would “take parliamentary action against him at that point” either through legislation or a no-confidence vote.

Corbyn also underlined the Labour stance that he should lead any temporary government were Johnson to lose a confidence vote.

“Of course: I’m the leader of the opposition,” said Corbyn. “All the British parliamentary precedents, going back as far as you care to look, are that the first option is that the leader of the opposition be invited to form an administration.”

As the Scottish National party gather for its annual conference in Aberdeen, Corbyn denied Labour would consider a formal coalition with the SNP after a general election. “We’re not going into coalition with anybody,” he said.

Asked about the possibility of Labour supporting a fresh Scottish independence vote, he said: “We would certainly not countenance it in the early days, or early years, of a Labour government, because I think the 2014 referendum was supposed to be a once in a lifetime opportunity.”