Sajid Javid said he would like to see the government do more on tax cuts, adding to the pressure on Boris Johnson from senior Conservatives after the damaging revolt over his leadership.
The health secretary said he thought Conservative MPs were prepared to get behind the prime minister, but he said it would be grossly unfair to change the rules to allow another vote on ousting him.
He added to other senior Tories calling for tax cuts, which Johnson had promised as he addressed his MPs in an attempt to save his leadership on Monday.
Javid said on Wednesday on BBC Radio 4's Today programme that they wanted to see us do more on tax cuts and I think every member of the government, all of my colleagues, we want to see taxes as low as possible.
There have been targeted tax cuts already. Some 70% of people, those who are less paid, will pay less national insurance than before because of the recent budget, I think I am right in saying that. When it was put to him that the tax burden was rising, he cited the challenges of the epidemic. He said that he would like to see cuts where they are possible. The chancellor will look at this because the government is taking it very seriously and I know that it is something that the chancellor will look at. Johnson and his chancellor, Rishi Sunak, will be speaking on the economy next week, but it is not clear if they will outline any specific tax cuts beyond outlining a broad direction of travel.
A No 10 source made clear that the economy speech would not include new personal tax cuts, as demanded by many backbenchers, saying it will not be anything fiscal.
It's a very difficult balance because everyone wants to cut taxes, but we also have to be fiscally responsible, according to the source.
A string of high-profile MPs, from Steve Baker in the party's right wing to Damian Green on its left backed a fresh demand from the Adam Smith Institute for the government to reduce the tax burden.
Since Monday's vote, Johnson won by 211 votes to 148, he has tried to draw a line under discontent in his party. Some critics of his leadership have vowed to carry on opposing him and have discussed changing the rules of the Committee of Backbenchers in 1922 to allow another confidence vote within the next 12 months.
Javid said that the rebels against Johnson should not try to change the rules, which state that a prime minister can't face another confidence vote for 12 months.
He told Times Radio: "I think most people would think that if you changed the rules it would be grossly unfair, it would be the wrong thing to do." I wouldn't support that, and if anyone wants to exercise the current rules, which they did, that's totally their right and I respect my colleagues for that, but the decision has been made. Javid described the vote as a clear win for the prime minister. He said that some people who voted against Johnson were now prepared to get behind him: Some I spoke to that publicly said they didn't support the prime minister in the vote, but they are democrats like all of us and they accept the result of the vote and they're getting behind the prime minister.