Nicola Sturgeon has ruled out holding an unofficial Scottish independence referendum, after her deputy suggested she could call one without legal approval.

Video footage emerged on Thursday showing Keith Brown, the deputy leader of the Scottish National party, telling independence activists: “If we want to have a referendum, then we decide we’re going to have a referendum.”

He said the SNP should not be put off because of a probable refusal by Theresa May to grant the necessary legal authority via a so-called section 30 order. “I don’t think the yes movement should be willing to anticipate a refusal of a section 30 order as a reason not to call a referendum,” he said.

As she faced opposition demands for clarification at Holyrood, Sturgeon insisted she had no plans to call a second referendum without a section 30 agreement, similar to the one agreed by the Scottish and UK governments in 2012, which paved the way for the 2014 vote.

“I am not open to that possibility,” she told reporters. “I want and consider that the basis of the referendum should be the same as the last time. [The] legal basis in future should be the same as the legal basis in the past.”

May has repeatedly stated she will not allow another referendum while Brexit is ongoing, a process she says will take several years. Asked at an event in Glasgow on Thursday whether permission would be given, Jeremy Hunt , the foreign secretary, said: “The answer of course will be no.”

Sturgeon’s spokesman said Brown had since clarified his position. In a tweet on Thursday morning, Brown said he meant the prime minister’s stance should not dissuade the Scottish government from seeking a section 30 order and trying to win the argument for one.

My position is clear - the deeply undemocratic stance of the UK Government in denying the mandate for indyref and refusing a s30 order should not prevent the Scottish Government seeking one and planning on the basis of winning that case. https://t.co/BTiQD9F50n — Keith Brown MSP (@KeithBrownSNP) March 7, 2019

His remarks, at an independence campaign event in Aberdeen last month, sparked allegations from the Scottish Conservatives the SNP was privately considering staging an illegal referendum, similar to the unofficial plebiscite held by Catalan nationalists in October 2017.

Many independence activists, backed by some SNP parliamentarians, believe Sturgeon is being far too timid and should stage a referendum without the approval of the UK government, and quickly. The acting leader of the Scottish Conservatives, Jackson Carlaw, said Brown was endorsing that stance in private.

“Nicola Sturgeon and Keith Brown are telling party activists one thing, while telling the public quite another,” he said. “In public, they tell us they’re focused on the day job. In private, they’re secretly plotting for an illegal referendum.”

Sturgeon’s advisers warn staging an unofficial referendum risks alienating wavering voters, could undermine confidence in her record of responsible government, and bog her government down in lengthy court battles. She could also be accused of illegally spending public money or overstepping Holyrood’s legal powers.

It is also highly likely to be boycotted by pro-UK parties and will not be recognised by foreign governments, financial institutions or businesses. While the SNP remains by far Scotland’s most popular party, support for independence stands at about 45%, despite the Brexit crisis.

Sturgeon is due to make a further speech in Holyrood on a second vote this month, once there is clarity over Brexit. She said last month “calm consideration” was needed.

Her spokesman said she would set out her precise thinking then, and denied the Scottish government was planning to hold a referendum without first getting a section 30 order. “She will set out the next steps when she sets out the next steps,” he said.

The SNP’s deputy leader, Keith Brown MSP. Photograph: Jane Barlow/PA

There is speculation Sturgeon favours delaying it until after the 2021 Scottish elections, but in Aberdeen Brown said Sturgeon had sympathy with hardliners’ arguments that any further delay would allow Brexit to become “normalised” in voters’ minds.

“The other thing that’s worth bearing in mind is, in 2021, if Brexit was to happen, and we didn’t go relatively soon, then the idea that Brexit might become normalised is quite a worry,” he said.

“People will get used to it, it will actually be normal. So, that, I think, I know, is also in Nicola’s mind.”