Boris Johnson has defended the government’s plans to cut universal credit while refusing to say whether he could live on the basic payment it provides of GBP118 a week.

Questioned by reporters during his trip to the US this week, the prime minister declined three times to answer whether he could survive on the UC payment.

Asked if he could live on GBP118 a week, and whether the cut, coming into force on 6 October, risked becoming a political problem, Johnson said: “I have every sympathy for people who are finding it tough, I really, really do.”

However, he said, not removing the GBP20 increase introduced amid the coronavirus pandemic would cost a lot. “We have to recognise that in order to maintain the Covid uplift you’ve got to find another GBP5bn to GBP6bn in tax. That has got to come out of some people’s pockets.

“Then I would just point out that the best solution is to continue to invest in people’s skills, to make sure that they are getting the type of jobs that reward their hard work – and you’re starting to see that, you’re starting to see wages go up. And that’s what we want to see.”

Johnson went on: “Wages are now rising faster than they have been for a long time, and the philosophy of this government is to try to deliver a high-wage, high-skill economy in which we invest in people, we invest in capital, we encourage businesses to put their profits back into people, back into the capital of the business, in order to drive productivity gain.

“And if you look at the UK since 2008, you look at our companies, they’ve been paying very low wages and they’ve been not investing, and productivity has fallen.”

Asked if his answer meant he could not live on GBP118 a week, Johnson replied: “It means that we want to support families in the best possible way.” Pressed on the fact this could be seen as saying no by default, he responded only: “Those are your words.”

Charities have warned the UC cut will push hundreds of thousands of people into poverty, exacerbated by rising energy costs. On Wednesday, the former prime minister Gordon Brown wrote in an article for the Guardian that the cut was the most “socially divisive and morally indefensible” he had witnessed in UK politics.

On Thursday it emerged that the Treasury is examining the possibility of tweaking the taper rate, under which wages below a low limit see UC payments docked in response, to allow people to keep more of what they earn.