SNP members should not be supporting an election candidate suspended by the party over alleged anti-Semitism, Nicola Sturgeon has said.

Neale Hanvey was the SNP's candidate for the Kirkcaldy and Cowdenbeath constituency but was dropped on November 26 after comments he made on social media over two years ago came to light.

Despite his suspension, Hanvey's name will still appear on the ballot paper next to the SNP name as the deadline for candidates to be nominated passed on November 14.

Speaking on the BBC'S Good Morning Scotland programme, SNP leader Sturgeon said it is right a disciplinary process against Hanvey is allowed to take its course.

"That's up to a disciplinary process now and it would be wrong for me to say anything that prejudiced that," she said.

"We made a very robust decision - I think the right decision - when his comments, the anti-Semitic comments, came to light, we suspended him.

"He's not the SNP candidate in that constituency but what happens after that is for a disciplinary process that is independent of me and I think it's right that that's allowed to take its course."

Scottish Labour's candidate for the constituency, Lesley Laird, claimed Hanvey is still using SNP branding in his campaign despite his suspension, while some SNP members are continuing to support his campaign.

Sturgeon said: "I've been very clear, I've said it publicly, I'll say it again - SNP members in that constituency should not be supporting his campaign, they should be going to other neighbouring constituencies to campaign for candidates there.

"The SNP could not have been clearer here, these are not easy situations for any party to find themselves in but you have to do the right thing.

"We've done the right thing here, I regret that we were in this position but he's not an SNP candidate, he shouldn't be using SNP materials, I haven't seen any evidence of that, and that's very clear.

"We've taken that (decision) because we have a zero tolerance to anti-Semitism and that's the right and important decision and position we took."

She added: "I'm not going to sit here and have disciplinary processes live on air.

"We will deal with anything that is brought to us in terms of the conduct of any member and we will do that fairly and robustly."

Last week, a member of the SNP's conduct committee, Denise Findlay, who was set to investigate Hanvey, quit the party after being challenged over alleged anti-Semitic content she posted online.

Sturgeon said the SNP would always do what it considers necessary to eradicate any form of racism, anti-Semitism or Islamophobia.

"When things come to light, we deal with that and that's perhaps the difference between the SNP and some other parties on these issues," Sturgeon said.

"No part of society can claim to be absolutely immune but we've got a duty, all of us, to eradicate these things and the SNP will always do what we consider necessary to do that and I think that's important that all parties take a similar view."

Speaking earlier to the BBC, Hanvey said: "I'm very sorry for any offence that's been caused, that was never my intention."

If elected, Hanvey said he would represent the community to the "best of his ability" as an independent MP, although said that would be a matter for the party to decide.

Asked if he would like to be readmitted to the SNP, he said: "Of course. The SNP is an incredibly important part of my life."