She went on: "Ecstasy is a dangerous drug and we are not saying in any way that it isn't.
A report from the independent Police Foundation had recommended an end to prison sentences for users of such drugs and other wide-ranging changes.
Ministers also ruled out calls for the reclassification of the two drugs, but they said other recommendations would be considered.
Mr Hellawell told a conference in Brighton: "There will be no change in the categorisation of cannabis and ecstasy. We see no justification for it. It would not improve the situation, it would make it worse."
But the report does not suggest any drugs should be legalised.
The two-year study was carried out by a panel including drugs experts, police officers and senior lawyers.
It argues that current laws have had limited success in deterring people from taking drugs.
The inquiry, called Drugs and the Law, recommends that heroin and cocaine remain Class A drugs, but cannabis should be transferred from Class B to Class C.
And it calls for a new offence targeting persistent drugs dealers and greater confiscation of assets from traffickers.
On prison sentences, the inquiry recommends they should be abolished for possession of Class B and C drugs, while the maximum prison sentences for possession of Class A drugs should be reduced.
The report also proposes an end to the ban on the therapeutic use of cannabis for specified medical purposes.
'Accurate messages'
Lady Ruth Runciman, the former head of the government's drug advisory council who chaired the report committee, said the foundation wanted a shift in balance "towards treating use as a health problem, not a crime problem and becoming tougher on those who traffic".
She went on: "Ecstasy is a dangerous drug and we are not saying in any way that it isn't.
"What we're concerned to do is to deliver accurate messages about it and to ensure that young people do not devalue the most dangerous drugs of all ... heroin, opiates and cocaine."
But Mr Hellawell said the depenalisation of cannabis would be problematic.
"What happens if someone is caught in possession of cannabis on a number of occasions? If you have no sanction apart from a slap on the wrist you have virtually decriminalised it."
Downing Street had already indicated that the government was not prepared to soften its stance on drugs.
The prime minister's official spokesman, Alastair Campbell, said ministers had made it clear that relaxing the laws would send the wrong signal.
Responding for the Home Office, minister Charles Clarke defended the government's decision.
'Deeply flawed'
He said to reform the drugs laws would "send the message that some from of drug taking is in some way acceptable".
Mr Clarke added: "That would be a deeply flawed message to send to young people."
But responding to the report for the Liberal Democrats, party leader Charles Kennedy welcomed it, saying it was way ahead of most politicians' thinking on the controversial issue.
Mr Kennedy, whose party have called for a Royal Commission on drugs, also called for a "fresh look" at allowing doctors to prescribe cannabis to their patients if necessary.