Mr Clarke tonight wrote to the caller who challenged him this morning on Five Live, saying he was "sorry" if his comments upset her.
In an excerpt from the letter released by his office, the Justice Secretary said: "I have always believed that all rape is extremely serious, and must be treated as such.
"I am sorry if my comments gave you any other impression or upset you."
Labour leader Ed Miliband demanded Mr Clarke's sacking after a series of broadcast interviews in which the Justice Secretary defended controversial Government proposals to halve the sentences of some rapists if they made early guilty pleas.
Under pressure from 10 Downing Street, Mr Clarke was forced to return to the TV studios to clarify his remarks.
While he did not apologise for his comments, the Justice Secretary insisted that he had not intended to cause offence.
He told Sky News: "Obviously , I don't intend to give the impression and didn't intend to choose words which gave the impression that all rape is not serious.
"Every rape is serious. That's always been my view and that's why I haven't the faintest intention of changing the sentence for rape."
Mr Clarke said he would look back at the transcripts of his interviews, adding: "Obviously it's a mistake if I gave the impression I have any other views."
The Ministry of Justice released a statement, in which Mr Clarke said: "My view has always been that all rape is a very serious crime, with appalling consequences for victims, and I certainly didn't mean to give any other impression. Any rape deserves to be punished with the full force of the law.
"I and the Government are absolutely clear that we are not proposing - and never have proposed - to reduce the sentences available for rape, or any other crime."
The row was sparked by an interview on BBC Radio Five Live, in which Mr Clarke angrily rejected reports that new plea-bargain arrangements could result in sex attackers facing just 15 months behind bars.
Asked why rape sentences were on average only five years, he said: "That includes date rape, 17-year-olds having intercourse with 15-year-olds.
"A serious rape, with violence and an unwilling woman, the tariff is much longer than that. I don't think many judges give five years for a forcible rape, frankly."
Asked if he thought date rape did not count as a "serious" offence, he said: "Date rape can be as serious as the worst rapes but date rapes, in my very old experience of being in trials, they do vary extraordinarily one from another and in the end the judge has to decide on the circumstances."
Put to him that "rape is rape", he said: "No, it is not."
Mr Clarke said he "could not think of a better example" than rape as an offence where it would be welcome to secure an early guilty plea, in order to spare victims the ordeal of going over the attack again in court.
In a later interview with Sky News, Mr Clarke described some offences as a "proper rape case".
"These are scare stories," Mr Clarke said. "No one is saying a serious, proper rape case is going to be let out of prison after 12 months."
Labour leader Ed Miliband seized on his remarks at Prime Minister's question time in the Commons, demanding David Cameron sack the veteran Cabinet minister by the end of the day.
Mr Miliband said the Justice Secretary "cannot speak for the women of this country when he makes comments like that" and should be removed immediately from the high-profile role.
Mr Cameron said he had not heard the interview but rape was "one of the most serious crimes that there is and it should be met with proper punishment".
The "real disgrace" was that only 6% of reported rape cases ended in a conviction, he said - insisting the Government was taking action to improve that rate.
A Downing Street source said they were sure Mr Clarke "will be clarifying his remarks to make sure everybody knows how seriously he takes rape in all its forms".
So long as he did that, his position was not in question, she indicated.
On his return to the Sky studio, Mr Clarke was pressed repeatedly to say whether he would apologise for his remarks.
He responded: "I will have a look when I get the chance at the transcripts of what I said.
"If I have given the impression that I do not regard all rape as a serious crime, I will sit down and have a look at it and see how on earth I gave that impression.
"I will make sure I give my views more clearly in future."
He said his intention had simply been to explain that sentences for rapists vary from case to case, depending on the circumstances surrounding the offence.
At present, admitting an offence immediately can qualify for a discount of a third of a sentence.
Supporters of the reform say it spares victims having to relive their ordeals in court but Mr Miliband said it was opposed by judges, campaigners and the Government's own victims' commissioner.
"Rape is such a serious offence and you should wait for the outcome of the consultation rather than just jumping on the bandwagon," Mr Cameron told him.
The Prime Minister left open the possibility that rapists could be excluded from the move to increase the sentence reduction for early guilty pleas - noting that it was still up for consultation.
Paul McKeever, chairman of the Police Federation which represents rank-and-file officers in England and Wales, said the Government should not be using "veiled and hidden discounts that the public don't understand and neither do I" in sentencing.
Asked if Mr Clarke should resign, he said: "It's not for me to say whether or not he should be in his place. Perhaps he will review and reflect on what he has said and look at it from a different perspective."
Pressed repeatedly to say whether he would apologise for his remarks, Mr Clarke said: "I will have a look when I get the chance at the transcripts of what I said.
"If I have given the impression that I do not regard all rape as a serious crime I will sit down and have a look at it and see how on earth I gave that impression.
"I will make sure I give my views more clearly in future."
He said he was "astonished" he could have given such an impression.
Judges gave different lengths of sentences "according to the circumstances and the offender" and "you can get a very bad case of rape", he said. "That's why the tariff starts at 10 years."
But he added: "The starting point as far as I am concerned is that all rape is a serious crime. There is no such thing as a trivial rape."
Mr Clarke insisted he had been right to question the idea put to him by the first interviewer that rapists were sentenced to an average five years.
"I was, as it turns out afterwards, correct in pointing out that the average sentence is eight years which is very much longer than the interviewer believed."
The Justice Secretary admitted he was unsure whether he had been right to claim that consensual sex between a 17-year-old and a 15-year-old was classified as rape.
"It may be 13 - I will check," he said, noting that all underage sex was a serious sexual offence.
Mr Cameron's official spokesman said later that Mr Clarke had the Prime Minister's confidence.
At a regular daily media briefing in Westminster, the spokesman refused to discuss whether the Prime Minister had spoken personally to Mr Clarke and ordered him to go back on to the airwaves to explain himself.
But he added: "I think he thinks it was important - as does the Justice Secretary - that the Justice Secretary went out and clarified the position."
Asked if the Prime Minister thought Mr Clarke should apologise, Mr Cameron's spokesman said: "I think the Prime Minister would say that if people have been offended by these comments, then that is clearly regrettable.
"But our position is very clear. We think rape is a very serious crime. Serious crimes deserve serious punishments and we have yet to set out policy in this area."
The spokesman stressed that the Government's final proposals on the extension of plea-bargaining had not yet been announced, and appeared to leave the door open for amendments before they are confirmed.
"We are not setting out the policy imminently and clearly we continue to listen to people's views," he said.
Labour MP Bridget Phillipson, who previously ran a refuge for the victims of domestic violence, said the Justice Secretary was "on the side of rapists".
"We are already in a less than perfect situation where unfortunately many women do not report rape and it does not result in criminal prosecution.
"So for the Justice Secretary to say that in effect he is on the side of rapists and not on the side of victims sends out absolutely the wrong message."
Ms Phillipson told BBC Radio 4's PM programme that Mr Clarke had undermined years of work to encourage victims to come forward.
Repeating the calls for his resignation, she said the discount policy was "not about supporting victims".
