Boris Johnson has said anyone who thinks there was something "dodgy or rum" in his dealings with Sir James Dyson is "out of their mind".
The PM was responding to claims by Labour that he was personally involved in "sleaze" after texts between the two were revealed by the BBC.
Downing Street declined to comment on "speculation" Mr Johnson's former aide Dominic Cummings had leaked the texts.
The government has launched an internal inquiry into who was responsible.
The prime minister's spokesman said: "We don't get into detail of processes in terms of these inquiries, but the Cabinet Office is taking that work forward."
The BBC said it did not discuss the sources of stories.
Mr Johnson was speaking on a visit to Derbyshire as allegations of cronyism abound at Westminster.
On Tuesday the BBC published text messages between Mr Johnson and Sir James, in which the prime minister agreed to "fix" concerns the businessman had over his employees' tax bills if they moved to the UK to make ventilators at the start of the pandemic.
Asked whether this proved Labour's allegation that friends of the Conservatives were given privileged access, the prime minister said it was "completely the right thing to do" to ask manufacturers to help bolster supplies of equipment needed to treat Covid patients.
"To think that there's anything remotely dodgy or rum or weird or sleazy about trying to secure more ventilators at the time of a national pandemic and doing everything in your power to do that, I think you're out of your mind," he added.
But Labour leader Sir Keir Starmer, who was on a visit to Hartlepool, said it was "increasingly obvious" the prime minister was involved in "sleaze".
Asked if media reports pointing to Mr Cummings as the source of leaks were part of an attempt to distract from lobbying allegations, Sir Keir said: "Boris Johnson is desperate to try to keep this at arm's length but it's obvious that he can't. This is government by WhatsApp.
"They are all at it - whether it's access to the prime minister, whether it's the former prime minister accessing ministers and officials, whether it's the health secretary with shares in companies with the contracts with the NHS. The list just grows and grows...
"Sleaze is back and it's bigger than it was before."
Shadow Treasury minister Bridget Phillipson tweeted: "Dominic Cummings is a distraction. Follow the money, not the soap opera."
Mr Cummings has not accepted invitations to respond to the reports and, so far, no evidence of his involvement in the leaks has been produced.
Labour has called for an urgent investigation into the prime minister's conduct by the Liaison Committee of senior MPs.
It said the text messages showed Mr Johnson had offered a "tax break" to a "chum".
The head of the committee, Conservative MP Sir Bernard Jenkin, turned down the call for an inquiry, saying three other parliamentary committees were already looking at the issues.
He told Radio 4's Today programme ministers should not be "locked away in ivory towers" with people unable to contact them and should be able to carry out conversations about policy in private, as this would "stifle proper conversation".
"What's got to come out of this is obviously a system of managing conflicts of interest, which commands more public confidence, and is more rigorous, but also a balance," he added.
The SNP's Westminster leader, Ian Blackford, has written to the Cabinet Secretary, calling for officials to "secure and publish" all Mr Johnson's private correspondence on coronavirus contracts, and not just his texts with Sir James Dyson.
He said "such a narrow and limited internal investigation totally and utterly fails to address the scale of the scandal".