John Swinney, Scotland’s deputy first minister and one of the Scottish National party’s longest-serving senior figures, has called for the party to unite and focus on concerns of mainstream voters as he ruled himself out of the contest to replace Nicola Sturgeon. Swinney, who is widely respected among the SNP membership and was its leader 20 years ago, said the party needed “a fresh perspective” after Sturgeon’s shock resignation on Wednesday. Encouraging leadership candidates to “anchor the SNP in the mainstream of Scottish politics”, he told BBC Radio Scotland’s Good Morning Scotland: “We’ve got to keep ourselves very, very close to the priorities and the issues that matter to people in Scotland. Independence cannot be some abstract concept.” Asked about the divisions within the party caused by recent gender recognition changes – which have been blocked by the UK government – Swinney said unity was “absolutely critical”, adding: “When the party has been united, we’ve actually achieved phenomenal results for our party and for the people of Scotland.” But he said he had “no regrets” that the legislation had passed, adding: “It’s important that we address the concerns of communities within our country who are marginalised, who are isolated, and to face very significant challenges.” Following a meeting of the party’s national executive committee on Thursday night, candidates will have until next Friday to put their names forward. A six-week contest will follow, with ballots of 100,000-plus members closing on 27 March. The NEC also announced that a special party conference in March, where members would vote on Sturgeon’s de facto referendum plan after the supreme court ruled that Holyrood did not have the powers to run another independence vote without Westminster’s consent, would be postponed. On Thursday, MPs and MSPs from across the party, including potential leadership candidates, said the conference should be dropped or postponed to allow the next leader to decide their own strategy, with the consequence that efforts to stage another referendum could be delayed by at least five years. The Scottish health secretary, Humza Yousaf, told BBC Scotland he was “seriously considering” standing, adding that “a lot of people have been in touch” with him about it. He added: “If I did go for it and I did get selected by the membership then of course it wouldn’t just have an impact on me, it would have an impact on my family. I have got two young girls and a wife and a family and therefore I have got think about the impact on them too.” Angus Robertson, the party’s former Westminster leader and the bookmakers’ favourite, is also expected to be among the first to declare, with Humza Kate Forbes, the finance secretary – who is on maternity leave – also expected to join the race.