Humza Yousaf has emerged as the frontrunner to replace Nicola Sturgeon as Scotland’s first minister after pledging to uphold her socially progressive policy agenda. The Scottish health secretary said on Monday that he backed Sturgeon’s stances on same-sex marriage, abortion clinic buffer zones, banning conversion practices and on gender recognition changes, stating he would “absolutely” challenge the UK government’s block on Holyrood’s gender recognition bill. He said the UK government’s decision to block the bill, which recent polls suggest is supported by a majority of Scottish voters, was in reality “an assault, an attack” on Holyrood’s autonomy. He said: “Is somebody really going to suggest to me we should lay down and allow them to trample over the will of the Scottish parliament [on] a bill that had support from every single political party?” Yousaf’s hopes of succeeding Sturgeon were boosted after Angus Robertson, the culture secretary who was made the bookmakers’ favourite when Sturgeon said she would quit, announced on Monday morning that he would not be running. The most experienced of the potential contenders and a former leader of the Scottish National party at Westminster, Robertson said in a tweeted statement that as the father of two young children “the time is not right [to] take on such a huge commitment”. That is expected to make the contest a two-candidate race between Yousaf, 37, and Kate Forbes, 32, the socially conservative Scottish finance secretary, who confirmed on Twitter that she was standing to succeed Sturgeon. Ash Regan, a former minister who quit Sturgeon’s government in protest at her gender recognition legislation, and has offered to work with Alex Salmond’s breakaway Alba party, is also standing but is widely seen as an outsider. In a campaign video released just as Yousaf prepared to speak, Forbes did not mention Sturgeon by name but said she was a unifier who would make all members feel included. “Right now, we need someone with a grip on our economy and our finances, in the throes of a cost of living crisis,” she said, referring to her three years as finance secretary. Many observers believe it became clear to Robertson that he was not supported by senior figures inside the party, and that Yousaf was Sturgeon’s favoured successor. Yousaf disclosed in his opening speech he was one of the few people Sturgeon had spoken to in advance about her plan to resign. Robertson is widely blamed for mishandling Scotland’s census last year, which had to be extended after hundreds of thousands of Scots failed to fill in their returns. Yousaf said he had chosen to launch his campaign on Monday in Clydebank, a former shipbuilding town west of Glasgow, because his grandfather Muhammed Yousaf had his first job at the nearby Singer sewing machine factory after emigrating to Scotland in 1962. Yousaf said his candidacy to become first minister was proof of Scotland’s inclusive, diverse ethos. His grandfather “couldn’t have imagined, not in his wildest dreams, that his grandson would be running to be first minister of Scotland,” he said. “I believe I have the necessary skills to bridge divides.” Pressed by reporters on how he would resurrect the campaign for Scottish independence, Yousaf said he disagreed with Sturgeon’s decision to make the next Westminster general election a “de facto referendum” on independence. He said the SNP’s goal was to make independence “the settled will” of the Scottish people. Asked later how that would be measured, he refused to say but said independence could only be achieved through a legally recognised route – implying it must be achieved with an authorised referendum. Forbes, a Gaelic speaker and member of the socially conservative, evangelical Free Church of Scotland, has emerged as the favoured candidate of the SNP’s pro-business wing and is seen as a critic of abortion rights and uncomfortable with gender recognition and same-sex marriage. Yousaf, a practising Muslim, indicated that if Forbes became first minister and took a more conservative stance on social issues, he may not serve in her government. He stood on the SNP’s progressive manifesto, he said. “People can look at my track record, but I don’t legislate on the basis of my faith. I do what I think is the best for the country.” But he went further than Sturgeon on the controversy over Isla Bryson – who was convicted of rape while a man before self-declaring as a woman, spending several days in a women’s prison – by saying he did not believe Bryson was a trans woman. Bryson was “a deceitful, deceptive individual [who is] simply pretending to be trans for the sake of making their life easier”, Yousaf said.