Genocide is being committed in Sudan's Darfur region, the US House of Representatives says in a resolution.
Many refugees say the militia worked with Sudan's security forces
Pro-government Arab militias have forced more than one million black Africans from their homes and killed thousands, human rights groups say.
The US is proposing a UN resolution threatening Sudan with sanctions. Congress urged the Bush administration to seek a strong document.
The UN is obliged to take action if it accepts genocide is occurring.
Speaking later on Friday, President George Bush said: "We made our position very clear to the Sudanese government - they must stop Janjaweed (militia) violence, they must provide access to humanitarian relief for the people who suffer".
He said the US was working with the UN and African Union "to bring relief to the suffering people in that region".
Both US Secretary of State Colin Powell and UN Secretary General Kofi Annan have previously said they have not seen enough evidence to convince them there is a genocide in Darfur.
RESOLUTION ACTION POINTS
US to lead an international effort to prevent genocide in Darfur
US to consider multilateral or even unilateral intervention
Impose targeted sanctions
Establish a resettlement and rehabilitation fund
Sudan denies backing the militias, and has warned the US and UK not to get involved in another Iraq-style crisis.
The US Congress says the government must seek a UN resolution to authorise a multinational force to protect the displaced civilians and aid workers in Darfur.
The resolution of the US House of Representatives - adopted unanimously by 422 votes and 12 abstentions - says the Bush adminstration should call the atrocities in Darfur "by its rightful name: 'genocide'."
It urges the Bush administration to consider "multilateral or even unilateral intervention to prevent genocide should the United Nations Security Council fail to act".
Up to 100 people were allegedly buried here
Many of those who have fled their homes say Janjaweed militiamen patrol outside the camps, killing men and raping women who go in search of food or firewood.
Photographer Marcus Bleasdale says he has taken pictures of between 30 and 40 mass graves in Darfur, in which up to 100 people had been buried.
"As we looked along the horizon, we could see hands and heads sticking out of the trenches," he told the BBC.
"While the world debates, people die in Darfur," Kansas Republican Senator Sam Brownback was quoted as saying by Reuters news agency.
"We actually could save some lives instead of lamenting afterward that we should have done something."
But Mr Powell again accused the Sudan government of backing the militias and said bomb attacks were continuing.
"Since they turned it on, they can turn it off," he added. "We made it clear to them that there will be consequences if it is not turned off."
The draft US resolution calls on Khartoum to crack down on the Janjaweed militia, which are accused of carrying out thousands of rapes and killings in Darfur, or face further action, including possible sanctions.
Mr Annan said he believed the Security Council would back the US-sponsored draft resolution.
"The reactions are quite positive... My sense is that it will be successful," he said at a joint press conference with Mr Powell.
Sudanese officials warned against any meddling in the country's internal affairs.
"We don't need any [UN] resolutions. Any resolutions from
the Security Council will complicate things," said Sudan's Foreign Minister Mustafa Osman Ismail.
He likened US and British pressure on Sudan as similar to that put on Iraq before the war there.
Some 6,000 policemen have been sent to restore peace in Darfur but the BBC's Hilary Andersson says those who have fled their homes are afraid of "uniformed men of any kind".
They fear the policemen could be used to force them to return home and accuse Sudan's security forces of working closely with the militias.
Sudan has also promised to disarm the Janjaweed, but the US says this has not yet started.
Sudan blames the conflict on rebels who took up arms last year, demanding greater rights for Darfur's non-Arab groups.