Boris Johnson has refused six times to address claims he failed to declare a potential conflict of interest in how money was given to a US businesswoman while he was London mayor.
The Sunday Times said Jennifer Arcuri joined trade missions he led and was given £126,000 in public money.
She told the paper it was part of her role as a legitimate businesswoman.
However, pressed by journalists on a trip to New York, the now-prime minister refused to comment.
Labour has said Mr Johnson must give a full account of his actions.
The newspaper claimed Ms Arcuri moved back to the US in June 2018, but her latest company won a £100,000 grant intended for “English-based” businesses earlier this year.
The Sunday Times said it had found the registered address on the grant application form was a rented house in the UK and no longer connected to her.
The government has confirmed to the BBC it is investigating, but said the funds were awarded to a UK-registered company.
The Sunday Times also claimed one of Ms Arcuri’s businesses received £10,000 in sponsorship money from a mayoral organisation when Mr Johnson was in office, and she received a £15,000 government grant for foreign entrepreneurs to build businesses in Britain.
‘Right and proper’
Transport Secretary Grant Shapps said it was “perfectly normal” for entrepreneurs to join trade missions, aimed at promoting British businesses overseas.
He told the BBC: “British companies and entrepreneurs go on trade missions. It’s quite right and proper and I’m sure that’s exactly what’s happened there.”
The current London Mayor, Labour’s Sadiq Khan, said he has ordered City Hall officials to look into the allegations.
Journalists asked Mr Johnson about the allegations when travelling with him to the UN General Assembly in New York.
The PM – who was London mayor between 2008 and 2016 – told reporters he was there to “talk about what we’re doing in the UN and this country’s commitment to tackle climate change”, as well as “the crisis in the Gulf and any other issues that may arise”.
Asked again, he replied: “I’m here to talk exclusively about the work of the UN.”
Ms Arcuri was quoted by the Sunday Times as saying: “Any grants received by my companies and any trade mission I joined were purely in respect of my role as a legitimate businesswoman.”