The former Brexit secretary laid out his vision on Sunday as Michael Gove confirmed he would be joining the race to succeed Theresa May as Conservative Party leader.
Mr Raab told the BBC that negotiations with the EU need to be more "resolute" than before.
He said while he does not want a no-deal Brexit, Britain is in a weaker position if it is not willing to walk away from negotiations.
But Chancellor Philip Hammond warned that the next PM would be defying Parliament if they took the UK out of the EU with no deal.
Mr Hammond told the BBC's Andrew Marr show: "I think it would be very difficult for a prime minister who adopted no-deal as a policy - we are leaving with no deal as a matter of policy - to retain the confidence of the House of Commons."
He added: "How will they govern if they have defied Parliament on such an important issue?"
Some eight ministers have announced they will stand for the leadership following Mrs May's announcement that she will step down on June 7.
Speaking from his London home, Mr Gove said he will join an already crowded field after Foreign Secretary Jeremy Hunt and ex-Cabinet ministers Dominic Raab and Andrea Leadsom threw their hats into the ring.
He said: "I can confirm that I will be putting my name forward to be prime minister of this country.
"I believe that I'm ready to unite the Conservative and Unionist Party, ready to deliver Brexit, and ready to lead this great country."
As the Tory battle for Downing Street intensifies, Mr Gove's intervention is likely to cause concern to current front-runner Boris Johnson.
A spectacular fall out between the two former allies in the 2016 leadership contest helped destroy both men's chances of the top job.
Mr Gove is posing as a self-styled "unity candidate".
Mr Raab said on Sunday it is important to deliver Brexit before the next general election.
He said: "We are scheduled for 2022 and I think it's very important we get Brexit delivered before we go back to the polls."
When asked how to stop the Conservative Party falling apart and an early general election being called, he said the party needs to come together, sort out Brexit, then tackle the other issues people are concerned about.
He said he will push to renegotiate the Withdrawal Agreement.
Mr Raab said previous negotiations with the EU had not been "resolute" enough and no-deal should have been left on the table.
He said: "We were not resolute enough and we took no-deal off the table.
"I don't want a WTO Brexit.
"We put ourselves in a much weaker position in terms of getting a deal if you are not willing to walk away from a negotiation - it doesn't focus the mind of the other side."
He added: "I would fight for a fairer deal in Brussels with negotiations to change the backstop arrangements, and if not I would be clear that we would leave on WTO terms in October."
Earlier Tory leadership contender Esther McVey told Sky's Sophy Ridge on Sunday that there will be no further extensions and the UK must prepare for a no-deal Bresit.
She said Britain will leave the EU on October 31, with or without a deal.
"October 31 is the key date and we are coming out then, and if that means without a deal then that's what it means," she said.
"We won't be asking for any more extensions.
"If Europe wants to come back to us, the door is open if they want a better deal.
"Time is limited, we have to make sure we are ready to leave."
Mr Hunt has claimed his business background would help resolve Brexit.
He told The Sunday Times: "If I was prime minister, I'd be the first prime minister in living memory who has been an entrepreneur by background.
"Doing deals is my bread and butter as someone who has set up their own business."
Health Secretary Matt Hancock said he was running for leader because the party needs to look to the future and attract younger voters.
Meanwhile, Chief Secretary to the Treasury Liz Truss has said she will not stand for the leadership.
She told the Sunday Telegraph she will back a contender who supported Leave in the 2016 referendum.
Labour has said it will trigger a Commons no-confidence vote in the new prime minister when they take office.
The new Tory leader looks set to take over as prime minister at the end of July after Mrs May finally laid out a timetable for her exit from Downing Street.
The timetable for the contest will see nominations close in the week of June 10, with MPs involved in a series of votes to whittle down the crowded field to a final two contenders.
Tory party members will then decide who wins the run-off.