Prof. Nutt, chairman of the Advisory Council on the Misuse of Drugs, attacked the decision to make cannabis a class B drug.
It is understood Home Secretary Alan Johnson asked him to consider his position in the wake of the comments, saying he had "no confidence" in him.
In a lecture and briefing paper for the Centre for Crime and Justice Studies at King's College, London, Prof Nutt attacked what he called the "artificial" separation of alcohol and tobacco from other, illegal, drugs.
He accused former home secretary Jacqui Smith, who reclassified cannabis, of "distorting and devaluing" scientific research.
Prof Nutt said smoking cannabis created only a "relatively small risk" of psychotic illness.
And he claimed advocates of moving ecstasy into class B from class A had "won the intellectual argument".
All drugs, including alcohol and tobacco, should be ranked by a "harm" index, he said, with alcohol coming fifth behind cocaine, heroin, barbiturates, and methadone.
Tobacco should rank ninth, ahead of cannabis, LSD and ecstasy, he said.
He also repeated his claim that the risks of taking ecstasy are no worse than riding a horse.
Ms Smith's decision to reclassify cannabis as a "precautionary step" sent mixed messages and undermined public faith in Government science, he said.
He added: "I think we have to accept young people like to experiment - with drugs and other potentially harmful activities - and what we should be doing in all of this is to protect them from harm at this stage of their lives.
"We therefore have to provide more accurate and credible information.
"If you think that scaring kids will stop them using, you are probably wrong."
Richard Garside, director of the centre for Crime and Justice Studies at King's College London, which published the article, accused Mr Johnson of undermining scientific research.
He said: "I'm shocked and dismayed that the home secretary appears to believe that political calculation trumps honest and informed scientific opinion.
"The message is that when it comes to the Home Office's relationship with the research community honest researchers should be seen but not heard.
"The Centre for Crime and Justice Studies published David Nutt's analysis because we believed it to be in the public interest that high quality scientific research should inform public policy in relation to drugs.
"The home secretary's action is a bad day for science and a bad day for the cause of evidence-informed policy making."
Speaking to Sky News, Prof Nutt said he was disappointed by the decision but linked it to "political" considerations.
He said: "It's unusual political times, I suppose, elections and all that. It's disappointing.
"But politics is politics and science is science and there's a bit of a tension between them sometimes."
Prof Nutt attacked politicians for "misleading" the public.
He said: "My view is policy should be based on evidence and I would have thought most politicians, when they have a chance to make policy based on evidence, that would actually be something they would enjoy doing.
"It's a bit odd to make policy that goes in the face of evidence."
"The danger is they are misleading us. The scientific evidence is there, it's in all the reports we published.
"Our judgments about the classification of drugs like cannabis and ecstasy have been based on a great deal of very detailed scientific appraisal.
"To say that there should be different classifications to send messages - I find this very confusing."
He said cannabis was "not that harmful" a drug and repeated his warning to parents about the impact of alcohol on their children.
"My children are much more likely to die or be seriously injured from alcohol than any of those other drugs.
"The greatest concern to parents should be that their children do not get completely off their heads with alcohol because it can kill them ... and it leads them to do things which are very dangerous like kill themselves or others in cars, get into fights ... get raped, engage in other activities which they regret subsequently.
"My view is that if you want to reduce the harm to society from drugs, alcohol is the drug to target at present and all parents should be very aware of that."
Shadow home secretary Chris Grayling said: "This was an inevitable decision after his latest ill-judged contribution to the debate but it is a sign of lack of focus at the Home Office that it didn't act sooner given that he has done this before."
A spokesman for the Advisory Council on the Misuse of Drugs (ACMD) said: "We can confirm that Prof Nutt has resigned as chair of the ACMD.
"It will be announced in due course who will deputise until a new chair is appointed."
Speaking later on BBC Radio 4's PM programme, Prof Nutt strongly criticised the Government's attitude to scientific evidence.
"Gordon Brown makes completely irrational statements about cannabis being 'lethal', which it is not," he said, adding that there was no reason why policy should not be "evidence based".
Prof Nutt said he was "disappointed" by Mr Johnson's move because he had a "much better" relationship with him than with Jacqui Smith, his predecessor at the Home Office.
But he went on: "I'm not prepared to mislead the public about the harmfulness of drugs like cannabis and ecstacy.
"I think most scientists will see this as a further example of the Luddite attitude of this government, and possible future governments, towards science."
The Home Office said Mr Johnson had expressed "surprise and disappointment" over what Prof Nutt said earlier this week.
As ACMD chairman he should be providing independent advice and not "lobby for changes in policy actions".
A spokesman said: "The home secretary has asked Professor Nutt resign as chair of the ACMD.
"In a letter he expressed surprise and disappointment over Professor Nutt's comments which damage efforts to give the public clear messages about the dangers of drugs.
"As chair of the council his actions undermine its role and scientific independence.
"We fully support the work of the ACMD and remain committed to considering the independent advice and evidence it and other advisory bodies provide to the Government.
"However, the clear role of the chair of the ACMD is to provide independent scientific advice and not to lobby for changes in policy.
"We remain determined to crack down on all illegal substances and minimise their harm to health and society as a whole."
In his letter Mr Johnson said Prof Nutt had gone beyond providing evidence to "lobbying" for changes to policy.
"As chair of the ACMD you cannot avoid appearing to implicate the council in your comments and thereby undermining its scientific independence," he wrote.
"As Home Secretary it is for me to make decisions, having received advice from the ACMD.
"It is vitally important that the public understand the council's role and also understand what the Government is trying to achieve.
"It is important that the Government's messages on drugs are clear and as an adviser you do nothing to undermine the public understanding of them.
"As my lead adviser on drugs harms I am afraid the manner in which you have acted runs contrary to your responsibilities.
"I cannot have public confusion between scientific advice and policy and have therefore lost confidence in your ability to advise me as chair of the ACMD.
"I would therefore ask you to step down from the council with immediate effect."
Prof Nutt said in reply he was "extremely disappointed" to be asked to quit.
He said: "I believe my advice to you and your predecessors has been of the highest quality and in the best interests of the UK public.
"Whilst I accept that there is a distinction between scientific advice and government policy there is clearly a degree of overlap.
"If scientists are not allowed to engage in the debate at this interface then you devalue their contribution to policy making and undermine a major source of carefully considered and evidence-based advice."
Comments