The head of HM Revenue and Customs (HMRC) renewed his apology today for errors that have left millions of people facing demands for back-tax.
Dave Hartnett also announced that those who "engaged" with the process and agreed to repay sums owing would not be charged interest.
Mr Hartnett initially refused to apologise for the situation in an interview with BBC Radio 4's Moneybox programme last week. HMRC rushed out an apology soon afterwards.
Giving evidence to the influential Treasury Select Committee today, Mr Hartnett said he regretted his "insensitivity" in not recognising immediately that people affected deserved an apology.
"I know how to apologise, I've had to do it before," he said. "I did not do it then and I am sorry for that."
He said he was "specifically apologising for the situation in which people find themselves".
"I think we could have done better in helping taxpayers to prepare for this," he added.
Mr Hartnett said he had said sorry to Treasury ministers for the way he handled questions in the Moneybox interview.
HMRC chief executive Dame Lesley Strathie stressed that the situation had arisen from the increased accuracy of the new National Insurance and PAYE IT system.
She insisted the organisation was "fit for purpose", adding: "I understand... when something is portrayed in the media as a mistake that people lose confidence in our workforce.
"Personally, I would like to put on record that this is an annual reconciliation."
She added: "I do want put very clearly on the record that these are not mistakes by our workforce."
She stressed that HMRC was not issuing "demands for payment", but rather "assessments of the tax that has been paid".
Some 14,000 people had already been reimbursed tax that was overpaid, and the "bulk" of the nearly six million people affected should be notified by the end of December, Dame Lesley said.
"It is very unfortunate that we have failed in this story to make the point that 4.5 million people are going to receive a cheque before Christmas," she added.
She also disclosed that ministers had insisted on a system for exempting those who owed more than £2,000 from being charged interest.
"Ministers have asked us to put in place a new process where anyone who receives the form P800 and have more than £2,000 to pay the notification will tell them that we will write to them about arrangements to pay and if we agree with that customer that they will pay, then they will not be charged interest," Dame Lesley said.
Mr Hartnett added: "Only those who will not engage with us will be charged interest."
Dame Lesley defended the PAYE system, and said there would always have to be reconciliations at the end of the year.
"Any system on account will have to reconcile," she said. "What we are trying to do is minimise the number of people who have underpayments or overpayments at the end of the year."
The MPs heard that ministers had been formally alerted to the scale of reconciliations at the end of July, but were told informally "some weeks before".
An estimated 2.3 million people underpaid an average of more than £1,400 in income tax during the past two tax years due to mistakes in their Pay As You Earn (PAYE) tax code.
The 900,000 owing the least have had their debts written off, but ministers said the Government could not afford not to collect the rest.
Most people will have between one and three years to repay the money through their pay packets, but those with £2,000-plus bills face having to find the money within three months.
The wrong tax might have been paid if workers or employers failed to notify HMRC of a change of circumstances or the tax authorities did not act on information they were given.
More errors than usual have been thrown up this year due to the use of a new IT system alongside the decades-old PAYE income tax system.
The committee was told that the decision to disregard the debts of 900,000 who owed less than £300 had cost the taxman £160 million.
The HMRC representatives were unable to tell the MPs how much the latest concession to waive interest would cost.