The Scottish National party could support a second referendum on Brexit if there were guarantees Scotland could also hold another vote on independence, its Westminster leader has said.

Ian Blackford said the SNP wanted clear assurances that if a majority of Scottish voters again chose to remain in the EU but the opposite happened in the rest of the UK, then Scotland would not be forced to accept the result.

Speaking on the eve of the SNP’s annual conference in Glasgow, Blackford said the party would not countenance a repeat the 2016 EU referendum, when Scotland voted heavily to remain but had to face leaving the EU with the rest of the UK.

He said it would be “very, very difficult” for those campaigning for a fresh Brexit vote to deny Scotland a second independence referendum under those circumstances.

“We have to have the protection of knowing that if the UK has a second vote and we end up in the same situation as we had in 2016, we would be able to determine our own future. That would be only right and proper,” he said.

“There has to be the right for Scotland to call a second referendum on independence.”

This year’s conference is expected to be one of the most subdued of recent years, with Nicola Sturgeon, the party leader and first minister, still unable to make a final decision on whether to call for a new independence vote. She faces a difficult dilemma: choose between thwarting Brexit or pressing on with independence.

Barely 24 hours before the start of the conference, thousands of independence activists backed by some SNP MSPs marched to the Scottish parliament in Edinburgh on Saturday. The rally, organised by the unaligned group All Under One Banner, increases pressure on Sturgeon to prioritise independence over Brexit.

Backed by Blackford, Sturgeon is waiting until the terms of a Brexit deal become clearer, but she also has to decide whether to commit to backing a second Brexit referendum if that becomes the best way to block a bad deal.

Blackford said he and Sturgeon were sceptical about the chances of a second Brexit referendum being held because both Theresa May and the Labour leader, Jeremy Corbyn, opposed the option.

As the third largest party at Westminster, the SNP’s 35 MPs could have a crucial role in any knife-edge vote on the Brexit deal or a second EU referendum. Vince Cable, the Liberal Democrat leader, wrote to Sturgeon on Friday urging her to join his party by backing the People’s Vote initiative.

The People’s Vote campaign added to Sturgeon’s dilemma by releasing the results of a YouGov opinion poll of 665 SNP members on Saturday which found that 79% thought the party should support a second Brexit vote.

With Corbyn under pressure from party members to reverse his opposition to a second referendum, there are signs the SNP is shifting ground too. Sturgeon’s Brexit minister, Mike Russell, held what he described as interesting and informative talks with Hugo Dixon, a leading figure in the People’s Vote campaign, late last month.

Blackford confirmed that Sturgeon’s aides had also floated another option that would involve structuring a second Brexit referendum so that all four UK nations would need to vote the same way for the result to be valid. The SNP says it would mean no part of the UK would be forced to accept an outcome it did not support.

Other parties are highly unlikely to back the idea, however, because it would give the smaller nations an effective veto on the result.

Sources in the People’s Vote campaign have indicated they would resist such an arrangement because a second Brexit referendum would have to be based on “speed, simplicity and clarity”.

The SNP, which is run by Sturgeon’s husband, Peter Murrell, has decided there will be no debate on independence or Brexit at this year’s conference, but the first minister will need to face down demands from hardline independence activists and some MPs and MSPs to launch a second independence campaign soon.

The party has also been reeling from the disclosure that its former leader, Alex Salmond, is being investigated for the alleged sexual harassment of two women. He has launched legal action calling for a judicial review of the investigation of the allegations, which he denies, backed by a divisive crowd-funding campaign.

Several MPs and MSPs appeared on Salmond’s controversial chatshow on the Kremlin-backed channel RT on Thursday calling for another independence referendum “as soon as possible”. They ignored Sturgeon’s instruction to boycott the show because of the channel’s links to Vladimir Putin’s government, which did little to dispel speculation about dissent within SNP ranks.