Mark Carney has backed the prime minister’s call to rethink Britain’s economic policy and rejected the idea that criticism of the side-effects of unconventional measures amounted to an attack on the independence of the Bank of England.

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In his first public comments since Theresa May said there had to be a change to a system that was biased in favour of the asset-rich and those paying mortgages, Carney said: “I entirely agree with the spirit of what the prime minister said.

“I have long said that monetary policy has been overburdened. There needs to be a better balance of monetary policy, fiscal policy and structural policy.”

His remarks at the International Monetary Fund in Washington came as the chancellor, Philip Hammond, sought to counter the suggestion that the government was unhappy with Carney’s performance and was thinking of replacing him as governor.

Carney again refused to say when questioned at the event whether he intended to serve a full eight-year term or leave Threadneedle Street in 2018 after five years.

However, Hammond praised the way the Bank had responded to the turbulence that followed the EU referendum and said he would welcome Carney being in charge until 2021.

“The Bank of England is executing its remit as an independent central bank, and [the] monetary policy committee is the arbiter on monetary policy decisions, in my view very effectively. They helped us recover from the financial crisis,” Hammond said in a Bloomberg TV interview while on a visit to New York. “They have helped us to smooth the response to this shock that occurred on 23 June.

“Obviously, Mark Carney said when he took the job on that he wasn’t guaranteeing to stay for the whole eight years. He will make his decision in due course. And that is his decision. He made that very clear. But I certainly would welcome his decision to stay if that is the decision he makes.”

Carney said Hammond had already signalled his intention to reset fiscal policy in next month’s autumn statement, adding that May’s speech showed the government’s intention to change the structure of the economy. “There is to be a rebalancing of policy in the UK, which will be part of a rebalancing around the world,” he said.

The Bank held interest rates at 0.5% for more than seven years before reducing them to a new record low of 0.25% in its post-Brexit package of measures announced in August. In early 2009, it launched the asset-purchase programme known as quantitative easing to expand the amount of money in the economy, under which Threadneedle Street purchased £375bn of gilts over the next four years.

In August, the Bank announced that it was buying an additional £60bn of gilts and £10bn of corporate bonds.

In her speech to the Conservative party conference in Birmingham, May said the emergency action had been appropriate when the economy was deep in recession. However, she added that “there have been some bad side-effects”.

“People with assets got richer, people without them have suffered, people with mortgages have found their debt cheaper, people with savings have found themselves poorer. A change has got to come and we are going to deliver it,” she said.

Carney accepted that some had benefited more than others from QE. “Every monetary policy action has distributional consequences. It is not for the central bank to address these consequences. It is for the government to offset them if they choose to do so as part of an agenda of more inclusive growth.”