Mr Zahawi told the BBC that division would delay the growth plan and risk defeat at the next election.
But ex-culture secretary Nadine Dorries warned Ms Truss needed to be a "unifier", not a "disrupter".
Mr Zahawi's call for unity was echoed by other cabinet ministers in Sunday newspaper articles.
When asked if he could see a situation where the Conservatives oust Ms Truss, Mr Zahawi told the BBC's Sunday with Laura Kuenssberg: "No, I think what the party will do is get behind Liz Truss."
Calling delay "our great enemy", Mr Zahawi said the government had to focus on delivering its plan for economic growth and lowering energy bills, adding how it would "demonstrate in 24 months' time how we have delivered".
Mr Zahawi also accused Scottish First Minister Nicola Sturgeon of using "dangerous language" when she took a swipe at the Conservatives on the same programme.
Speaking ahead of the SNP's party conference in Aberdeen on Sunday, Ms Sturgeon said she would prefer a Labour rather than a Tory government, adding: "I detest the Tories and everything they stand for."
Ms Dorries told the programme the Tories faced electoral "wipeout" and urged the prime minister to "reflect on what's gone wrong" in recent weeks.
When asked about her suggestion in a tweet that the prime minister should call a general election if she wanted to drop the policies of Boris Johnson, she said if Ms Truss introduced a "completely new set of policy ideas", it would "be right to go to the country".
But she continued: "Liz doesn't need to do that. And I really hope she won't do that when we're 30 points behind in the polls [to Labour]."
Ms Dorries, who insisted she was "still one of Liz's biggest supporters", called on Tory colleagues to unify behind the prime minister.
The calls to cease the public divisions within the party follow a turbulent week for Ms Truss, with interventions from former ministers and backbenchers forcing a U-turn over plans to scrap the top 45p rate of tax on the highest earners.
Disagreements also emerged over calls to raise benefits in line with inflation.
When asked if Boris Johnson could return as prime minister, Ms Dorries said she did not "rule anything out" but it was "extremely unlikely".
Mr Zahawi said he could not see Mr Johnson returning, saying the former prime minister was "telling all colleagues to get behind Liz".
Mr Zahawi and other cabinet colleagues - including Home Secretary Suella Braverman and Commons Leader Penny Mordaunt - penned opinion pieces in Sunday's newspapers. Ms Braverman and Mr Zahawi both suggested any future Labour administration would be propped up by the SNP.
BBC political correspondent Ian Watson says No 10 is keen to quell any talk of rebellion among Conservatives as MPs return to Westminster this week after the party conference season.
But he says despite the co-ordinated messages from cabinet ministers, Ms Truss's internal critics could interpret the need for such explicit declarations of support as a sign of vulnerability.
Watch: I detest the Tories and everything they stand for - Nicola Sturgeon
Watch: Dorries quizzed over potential Boris Johnson return