David Cameron has defended the government's welfare changes in the face of criticism from the head of the Roman Catholic church in England and Wales, insisting they were part of his "moral mission" for the country.

The prime minister said claims by the archbishop of Westminster, Vincent Nichols, that recent changes to the benefits system had left many people facing hunger and destitution were "simply not true".

Writing in the Daily Telegraph, Cameron said the changes were not just about "making the numbers add up", but were intended to bring new hope to people who had previously been written off by the system.

"Our long-term economic plan for Britain is not just about doing what we can afford, it is also about doing what is right," he wrote. "Nowhere is that more true than in welfare. For me the moral case for welfare reform is every bit as important as making the numbers add up."

Cameron said that while the church was entitled to speak out on political issues, he did not accept the archbishop's claim that the system was becoming increasingly punitive and that the situation in which many people now found themselves was "a disgrace".

"Of course, we are in the middle of a long and difficult journey turning our country around," Cameron said. "That means difficult decisions to get our deficit down, making sure that the debts of this generation are not our children's to inherit.

"But our welfare reforms go beyond that alone – they are about giving new purpose, new opportunity, new hope – and yes, new responsibility to people who had previously been written off with no chance.

"Seeing these reforms through is at the heart of our long-term economic plan – and it is at the heart too of our social and moral mission in politics today."

The archbishop, who is to be made a cardinal later this week, defended his comments, saying he had been "inundated" with messages of support since speaking out last week.

"What I notice in government statements is that they are mostly cast in the future tense 'These reforms will achieve this, will achieve that,"' he told the Telegraph.

"My concern is to echo the voices that come to me of the circumstances today in which people are left without any support for weeks on end, are hungry, are destitute. There must be something wrong with the administration of a system which has that effect on so many people's lives."