They acknowledged, however, that the bill has virtually no chance of becoming law.
"We believe the federal government shouldn't be involved with prosecuting adults smoking marijuana," said Democratic congressman Barney Frank today. "We don't have enough prosecutors or police officers to do so."
The bill is the first ever effort to legalise the production and consumption of marijuana nationwide.
Sixteen states and the District of Columbia have legalised the production and consumption of marijuana for medical purposes, while 14 states have decriminalised small amounts for consumption.
"I don't expect to pass it in this Congress," added Mr Frank. "But I think we're making progress. This is an educational process." About 850,000 Americans were arrested in 2009 for marijuana-related offences, and about 90 per cent of those cases were for possession, according to figures from the FBI.
"The drug war has not worked, clearly," said Jared Polis, a Democrat from Colorado.
The Obama administration's Office of National Drug Control Policy, which opposes legalisation, contends that marijuana potency has tripled in the past 20 years and that the age of teen drug users is getting younger.
It also says that 30 per cent of people who have used marijuana in the past year say they are dependent on the drug.
Mexican President Felipe Calderon, whose country is the main supplier of marijuana and amphetamines to the United States, warned recently that legalising cannabis would make it tougher for countries like Mexico to prosecute farmers for growing a product that was legal in the United States.
"I would say to President Calderon that he does what he thinks is right in Mexico and I'll do what I think is right in the United States," said Mr Frank, who said the bill would not allow the importation of the drug.
But, he said, the legalisation of cannabis in the United States, the biggest drug consuming country in the world, would "produce a shift in the market".
Three weeks ago a group of ex-presidents of Latin America as well as former United Nations Secretary General Kofi Annan denounced the failure of the global war on drugs and called for urgent changes, including the legalisation of cannabis.