David Cameron has said he should have contacted the government “through only the most formal of channels” when lobbying for a financial firm.
The former prime minister has faced criticism for contacting ministers on behalf of Greensill Capital.
In his first statement on the issue, he said he should have left “no room for misinterpretation”.
He added: “However, I have reflected on this at length. There are important lessons to be learnt.”
The Labour Party said Mr Cameron’s statement had left “many serious questions” unanswered, and called for him to answer them before Parliament.
It was revealed earlier that Health Secretary Matt Hancock had met Mr Cameron and financier Lex Greensill for a “private drink” in 2019 to discuss a new payment scheme for the NHS.
The meeting is the latest in a series of Sunday Times disclosures about Mr Cameron’s lobbying work since leaving office, with Chancellor Rishi Sunak – whom he texted – among the ministers contacted.
Mr Greensill, an Australian, worked as an unpaid adviser to Mr Cameron’s government, and the former prime minister went on to be employed by his company – Greensill Capital – in 2018, two years after leaving Downing Street.
In his statement, Mr Cameron said: “In my representations to government, I was breaking no codes of conduct and no government rules.
“Ultimately, the outcome of the discussions I encouraged about how Greensill’s proposals might be included in the government’s CCFF (Covid Corporate Financing Facility) initiative – and help in the wake of the coronavirus crisis – was that they were not taken up.
“So, I complied with the rules and my interventions did not lead to a change in the government’s approach to the CCFF.”
He added: “As a former prime minister, I accept that communications with government need to be done through only the most formal of channels, so there can be no room for misinterpretation.”
Mr Cameron added that he had worked for Greensill Capital in the belief that there “would be a material benefit for UK businesses at a challenging time”.
“That was, in large part, my reason for working for Greensill in the first place,” he said.
The company recently collapsed, with the loss of 440 jobs.
Mr Cameron said: “I completely understand the public interest in this issue, given the impact of Greensill’s collapse on the hundreds of people who worked for the company and on other businesses and livelihoods. I feel desperately sorry for those affected.”
Labour’s Gordon Brown who was prime minister from 2007 to 2010 – said: “Former prime ministers must never be lobbying for commercial purposes. Current ministers should not be entertaining such lobbying.”
If it could not be stopped, he told BBC Radio 4’s Today programme, new laws should be passed to stop former ministers lobbying for five years after leaving office.
“It simply brings public service into disrepute,” added Mr Brown.
Labour is calling for Mr Cameron to appear before Parliament to answer questions about the “scandal”.