Ahead of the second round of voting on Tuesday, Mr Raab hit out at those in Parliament who he accused of trying to “steal” Brexit from the voters.
He defended his controversial refusal to rule out suspending Parliament to prevent it blocking a no-deal saying he did not want to weaken his negotiating position with the EU.
However, fellow leadership contender International Development Secretary Rory Stewart accused rivals pledging to leave by October 31 of making promises they could not deliver on.
Foreign Secretary Jeremy Hunt said that committing to a “hard stop” at the end of October would be to ensure a no-deal Brexit.
He said he believed he could negotiate a new deal with the EU which would avoid the need for the Northern Ireland backstop, which led to Theresa May’s deal being defeated three time in the Commons.
Mr Raab, who, like Boris Johnson, is committed to leaving by October 31 with or without a deal, insisted there could be no more delay to Brexit.
“The Tory Party will be toast unless we are out by the end of October. The Conservatives cannot win an election unless we have delivered Brexit,” the former Brexit secretary told Sky News’s Ridge On Sunday programme.
He again refused to rule out proroguing Parliament if it was necessary to ensure that MPs could not “sabotage” the will of the people.
“The big mistake we made in these negotiations was taking no-deal off the table. When we start ruling things out we only weaken our chances of getting a deal,” he said.
“All those candidates that are going weak at the knees and saying ‘I’m not sure about this and that’, they are sending a message to the EU that they can take us for a ride.
“We gave people a decision. Now Parliament is trying to steal it back away from them. When people voted, they voted to leave.”
Mr Stewart launched a fresh attack on Mr Johnson, who has come under fire for avoiding media scrutiny, warning his plans would “come off the rails” once they were subjected to detailed examination.
“How is Boris going to deliver Brexit? He keeps saying ‘I am going to deliver it’. I don’t even know what he believes. He won’t talk to me. He won’t talk to you. He won’t talk to the public,” he told BBC1’s The Andrew Marr Show.
“We live in parliamentary democracy. I am campaigning against candidates who are pretending we are living in the United States and we are going for presidential politics where some big man just says ‘This is going to happen’.
“We are a moderate country, we are not a Trumpian country.”
Mr Stewart said that ultimately the best way to deliver Brexit was to return to Mrs May’s deal.
“It know that this feels terrible to people because they have seen that defeated again and again. But it is the quickest, the most constitutional, the most legitimate way of getting it done,” he said.
Meanwhile, Mr Hunt said it would “difficult but not impossible” to negotiate a new deal with Brussels which could get through Parliament.
“When you talk to European leaders as I do, they want to solve this problem,” he told The Andrew Marr Show.
“They say that if they were approached by a British prime minister, someone they were willing to deal with, who had ideas how to solve the Northern Irish border, they would be willing to re-negotiate the package.”
Mr Hunt said it could even be done by the deadline of October 31, but added that it would be a mistake to commit to leaving the EU by that date.
“If you do make that guarantee and you go with the wrong approach, then you are committing us to nothing other than a hard Brexit, a no-deal Brexit,” he said.