The goal of levelling up is to provide equal opportunities across the UK.
A BBC Panorama investigation raises questions about whether money is reaching the most deprived areas in England.
Mr Gove said his department was helping councils to ensure bids are effective.
"Unless we stick to those missions, then the cost of living issues that we face at the moment will deepen inequality," said Mr Gove.
Labour's Lisa Nandy, the Shadow Levelling Up Secretary, said the government should begin by getting inflation under control. "By their own admission, their mismanagement of the economy is going to make levelling up harder," she told the BBC.
For the first round of the so-called Levelling Up Fund, £1.7bn has been allocated to towns and cities across the UK.
A second round for the fund will open for applications at the end of May.
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