Rishi Sunak has failed to deny that cabinet members are among the Tories to place bets on the date of the election.
Three Tories with close links to the prime minister, as well as one of his close protection officers, are being investigated over the allegations.
The Conservatives have confirmed they “have been contacted have been contacted by the Gambling Commission about a small number of individuals”.
That has led to speculation that more Tories may be caught up in the scandal.
At the launch of the Tories’ Welsh manifesto today, Sunak repeatedly dodged questions about the affair.
He was asked by a reporter from LBC: “Are you confident none of your cabinet members have also placed a bet?”
The prime minister replied: “The first thing to say is I was incredibly angry when I learned about these allegations - the same anger that many of you will feel and everyone watching.
“It’s right that they are investigated thoroughly, these are serious allegations. Right that they are being thoroughly investigated, as they are being. Independently, including a criminal investigation.
“If anyone is found to have broken the rules, they should face the full consequences of the law.”
Darren McCaffrey of Sky News then asked the PM: “Can you hold your hand on your heart and say you are currently not aware of any other Conservatives that you know who may have placed a bet on the election?”
Sunak replied: “There’s not much more I can add to what I said previously. There are multiple investigations that are currently happening. It’s right that those investigations are allowed to proceed, they are independent, they are necessarily confidential.”
Katherine Forster of GB News pointed out that Keir Starmer has said that if any Labour candidates had been accused of putting bets on “their feet wouldn’t have touched the ground”.
She added: “You say there are investigations ongoing, but why don’t you suspend them in the meantime because you’re burning through huge amounts of political capital on this, aren’t you?”
But the PM said: “These are really serious matters, they’re being investigated by multiple authorities, including law enforcement, including a criminal investigation.
“You’ll know that those investigations are confidential and there is a limit to what can happen during those investigations to protect the integrity of them.
“I’ve made it crystal clear that the allegations have made me very angry, but it is right that those investigations are allowed to conclude properly.”
The Guardian first reported last week that Craig Williams, Sunak’s parliamentary aide before the election was called and the Conservative candidate in Montgomeryshire, was being probed by the Gambling Commission.
The scandal intensified when the BBC revealed that one of the PM’s close protection officers had been suspended after also allegedly placing a similar bet.
It then emerged that a second Tory candidate, Laura Saunders, was also under investigation by the Gambling Commission, as was her husband, Tony Lee.
He has taken a “leave of absence” from his role as the Conservatives’ campaign director.
Labour’s Jonathan Ashworth said: “Rishi Sunak has refused to rule out that further members of the Conservative Party, including cabinet ministers, are involved in this betting scandal. He needs to come clean with the public.
“He promised integrity, professionalism and accountability. Instead, his weakness means he has overseen the same levels of sleaze and scandal that have come to epitomise the last 14 years of Tory government.
“Rishi Sunak needs to take immediate action against all implicated.”