Rishi Sunak has said he is “not aware of any other” Conservative election candidates being investigated by the Gambling Commission over alleged bets on the date of the general election.

He has confirmed that his party is carrying out its own internal inquiries “in parallel” with the Gambling Commission’s investigation.

The commission has not said who it is investigating but so far the names of four Conservatives have emerged – including two who are standing for election.

Mr Sunak has come under pressure from opposition parties, as well as some in his own party, to suspend the two candidates.

Conservative Tobias Ellwood said the story was “deeply unhelpful” and that the public wanted to see “robust action”.

Labour leader Sir Keir Starmer said: “Rishi Sunak needs to show some leadership. If these were my candidates, I tell you what – they’d be gone. Their feet wouldn’t have touched the floor.”

He dismissed the Conservative Party’s internal inquiry as being “designed for one purpose, which is to knock this in the long grass to the other side of the election”.

Defending the PM, Northern Ireland Secretary Chris Heaton-Harris told the BBC people were not “guilty until they’re proven innocent” and that the regulators should be allowed to “get on with” the investigation.

The allegations of gambling on the election date first emerged earlier this month against Craig Williams – one of the prime minister’s closest aides, who reportedly placed a £100 bet on a July polling day three days before the date was named.

Mr Williams – who is standing for the Conservatives in Montgomeryshire and Glyndwr – told the BBC he had made a “huge error of judgement” but refused to say if he had placed a bet on the basis of inside information.

If someone uses confidential information to gain an unfair advantage when betting, this could be a criminal offence under section 42 of the Gambling Act.

Laura Saunders, the Conservative candidate for Bristol North West, and her partner Tony Lee, the Conservative director of campaigning, are also under investigation, as is Nick Mason, the party’s chief data officer.

Mr Mason’s spokesperson said he denied wrongdoing. Both Mr Mason and Mr Lee have taken leaves of absence from their party role’s.

The BBC understands the Gambling Commission’s inquiries involve more people than those publicly named so far and other people linked to the party of the government are being looked into.

Speaking to reporters in Edinburgh, Mr Sunak said he did not have the details of the Gambling Commission’s investigation but that his party was conducting its own “internal inquiries”.

He added he would “act on any relevant findings” and pass on information to the commission.

He also confirmed that he was not under investigation himself and that he had never placed a bet on politics whilst an MP.

On Monday evening, the prime minister was again pressed on the subject by the Sun newspaper’s political editor Harry Cole and whether he could simply question those he told about the election date before it was announced.

Mr Sunak said he did not want to “compromise the integrity” of other investigations but added: “I have been crystal clear – if anyone has broken the rules they should not just face the full consequences of the law but they will be booted out of the Conservative Party.”

Earlier in the day, Mr Ellwood, a Conservative candidate in Bournemouth East, said the scandal had been “deeply unhelpful”.

Asked if Mr Sunak should withdraw Conservative support from Mr Williams and Ms Saunders, Mr Ellwood said: “Given the scale of this as we see now, and the potential for this story to continue to eclipse, to overshadow the election, I would now agree.

“The public want to see clear robust action now.”

Conservative peer and former minister Jo Johnson told BBC’s Newsnight there was “immense frustration” amongst Tory candidates and activists that the story was still “rumbling on” because “Number 10 hasn’t managed to get to the bottom of it”.

He called for the PM to take “firm action”.

“Clearly no one can understand why people haven’t been suspended where in comparable situations others might have been,” he added.

Liberal Democrat leader Sir Ed Davey said: “I do think the Conservative Party could do far more.

“It feels to me like, as has been so often the case during this Parliament, they seem to be in it for themselves, not for the public service.”

On Sunday, Labour’s election coordinator Pat McFadden wrote to the Gambling Commission urging it to “make public the names of other figures” under investigation.

In a reply seen by the BBC, Andrew Rhodes, the regulator’s chief executive, said: “We understand the desire for information, however, to protect the integrity of the investigation and to ensure a fair and just outcome, we are unable to comment on any details at this time, including the name of any person who may be under suspicion.”