Rupert Murdoch has admitted he was wrong to describe phone-hacking and corrupt-payments investigations by police into his company and its journalists as "incompetent", in a letter sent to the chairman of the Commons home affairs select committee.

But writing to Keith Vaz, he has also questioned the proportionality of the investigations, which will have cost £40m by 2015 and have involved dawn raids involving up to 14 officers, and the arrest of scores of his journalists.

The letter marks the first time that the media chief has spoken about what he has termed a "highly emotional" meeting that occurred in March with journalists at the Sun who had been arrested and who face trial for allegedly paying public officials for information. The meeting was secretly recorded and subsequently leaked.

In his letter, which has been published by Vaz, Murdoch said: "I accept that I used the wrong adjectives to voice my frustration over the course of the police investigation. But I have been hearing for months about pre-dawn raids undertaken by as many as 14 police officers, and that some employees and their families were left in limbo for as much as a year and a half between arrest and charging decisions."

He said of the meeting on 14 March, requested by his staff: "I was reminded of the impact on families, including suicide attempts and medical conditions arising from the significant stress."

Recordings of the secretly recorded meeting were subsequently broadcast on the Exaro website.

Speaking to staff who were working for the Sun, Murdoch had said in the meeting: "Still, I mean, it's a disgrace. Here we are, two years later, and the cops are totally incompetent. So, I'll just ask you a question, I don't want to interrupt you – are you happy with the lawyers that have been provided?"

But there was a clear limit to his apology in the letter to Vaz. "I have no basis to question the competence of the police … but I do question whether, over the last two years, the police have approached these matters with an appropriate sense of proportion with regard for the human cost of delay.

"Whilst I regret my choice of words in that highly emotional meeting, I care deeply about our employees and I was and am troubled by the effect of these events on them."

The assistant commissioner of the Metropolitan police, Cressida Dick, revealed to Vaz's committee last week that detectives were seeking a copy of the tape whether anything Murdoch said at the meeting amounted to alleged conspiracy to commit misconduct in public office – an allegation not addressed by him.

But when he was asked to comment on Dick's claims that the police investigation was very competent and progressing well, Murdoch said: "I cannot endorse the judgment that the investigation has 'progressed' very well, not when some of our employees were arrested early in the investigation in 2012 and they and their families are still in limbo awaiting charging decisions … My personal view is that this has gone on too long."

Those comments were endorsed by Vaz. "Mr Murdoch's letter does raise the issue of the length of time these investigations have taken which the home affairs committee has raise and which have so far cost the taxpayer £20.3m," he said.

The tape recording also heard Murdoch indicating that News UK – owner of the Sun, and the former News of the World – was no longer co-operating fully with the investigations. Police said they were having to seek court orders for some information. said in the letter that he made the decision in 2011 to co-operate fully with the police because "we thought it was the right thing to do". He said that after volunteering a mountain of evidence, including 500,000 documents, a further 1,900 requests for information had been made by the police.

"Over 98% of these requests have already been resolved to everyone's satisfaction," he added.

Vaz said: "I am pleased to hear News UK are co-operating with the Metropolitan police, and hope they continue to do so. It is in everyone's interests for them to redouble their efforts to co-operate which will speed up the investigation process and bring it to a conclusion."

In a separate letter to John Whittingdale, chairman of the Commons culture and media select committee, Murdoch rejected claims he was aware of his journalists paying police for information. "The 'reports' that I knew about, let alone tolerated payments to police, are completely false," he wrote. He said he accepted that his journalists should face the consequences of violating the law but insisted his staff had "been singled out for the harshest treatment".

Murdoch offered to appear before Whittingdale's committee on 29 July to be interrogated over the tape, but it is understood he was told the MPs on the committee would be on holiday and not able to accommodate him.