Mr Shapps told the Sunday Times that if he is elected prime minister, he will not call a general election.
Mr. Zahawi has stated that he will cut taxes, increase defence spending, and continue education reforms that he began as education secretary.
Tories are rushing to take sides in the race to become the next Prime Minister, with six names now confirmed.
Rishi Sunak declared on Friday that he has set his sights on Downing Street.
Former Equalities Minister Kemi Badenoch has now entered the race, proposing a smaller state and a government “focused on the essentials.”
Defence Secretary Ben Wallace, widely regarded as a frontrunner, ruled himself out of the race on Saturday afternoon to “focus on [his] current job,” making him one of the party’s most valuable backers for whoever wins his support.
Meanwhile, former minister Steve Baker has backed Attorney General Suella Braverman’s campaign, which she announced on ITV’s Peston show.
While the chairman of the Commons Foreign Affairs Committee, Tom Tugendhat, has already stated that he will be putting his name forward.
Mr Shapps stated in The Times that his goal was to address the cost of living crisis and rebuild the economy.
When pressed on his loyalty, the Welwyn Hatfield MP stated, “I have not spent the last few turbulent years plotting or briefing against the prime minister.” I’m not organising a leadership campaign behind his back. I’ll tell you something: I like Boris Johnson despite his flaws – and who isn’t flawed? I’ve never had any doubts about his love for this country.