They are accused of forcing some one million people from their homes and killing at least 10,000.
Many thousands more are at risk of starving due to a lack of food in the camps where they have fled.
UN Secretary General Kofi Annan has refused to use the term genocide, which would carry a legal obligation to act.
But US Secretary of State Colin Powell said: "We see indicators and elements that would start to move you toward a genocidal conclusion but we're not there yet."
But what is genocide and when can it be applied? Some argue that the definition is too narrow and others that the term is devalued by misuse.
The term was coined in 1943 by the Jewish-Polish lawyer Raphael Lemkin who combined the Greek word "genos" (race or tribe) with the Latin word "cide" (to kill).
After witnessing the horrors of the Holocaust - in which every member of his family except his brother and himself was killed - Dr Lemkin campaigned to have genocide recognised as a crime under international law.
His efforts gave way to the adoption of the UN Convention on Genocide in December 1948, which came into effect in January 1951.
Article Two of the convention defines genocide as "any of the following acts committed with the intent to destroy, in whole or in part, a national, ethnical, racial or religious group, as such:
Killing members of the group
Causing serious bodily or mental harm to members of the group
Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part
Imposing measures intended to prevent births within the group
Forcibly transferring children of the group to another group
The convention also imposes a general duty on states that are signatories to "prevent and to punish" genocide.
Ever since its adoption, the UN treaty has come under fire from different sides, mostly by people frustrated with the difficulty of applying it to different cases.
Some analysts argue that the definition is so narrow that none of the mass killings perpetrated since the treaty's adoption would fall under it.
The objections most frequently raised against the treaty include:
The convention excludes targeted political and social groups
The definition is limited to direct acts against people, and excludes acts against the environment which sustains them or their cultural distinctiveness
Proving intention beyond reasonable doubt is extremely difficult
UN member states are hesitant to single out other members or intervene, as was the case in Rwanda
There is no body of international law to clarify the parameters of the convention (though this is changing as UN war crimes tribunals issue indictments)
The difficulty of defining or measuring "in part", and establishing how many deaths equal genocide
But in spite of these criticisms, there are many who say genocide is recognisable.
In his book Rwanda and Genocide in the 20th Century, former secretary-general of Doctors Without Borders, Alain Destexhe says: "Genocide is distinguishable from all other crimes by the motivation behind it.
"Genocide is a crime on a different scale to all other crimes against humanity and implies an intention to completely exterminate the chosen group.
"Genocide is therefore both the gravest and greatest of the crimes against humanity."
Mr Destexhe believes the word genocide has fallen victim to "a sort of verbal inflation, in much the same way as happened with the word fascist".
Because of that, he says, the term has progressively lost its initial meaning and is becoming "dangerously commonplace".
Michael Ignatieff, director of the Carr Centre for Human Rights Policy at Harvard University, agrees.
"Those who should use the word genocide never let it slip their mouths. Those who unfortunately do use it, banalise it into a validation of every kind of victimhood," he said in a lecture about Raphael Lemkin.
"Slavery for example, is called genocide when - whatever it was, and it was an infamy - it was a system to exploit, rather than to exterminate the living."
In the Democratic Republic of Congo, a renegade commander said he captured the town of Bukavu earlier this month to prevent a genocide of Congolese Tutsis - the Banyamulenge.
It later transpired that fewer than 100 people had died.
The differences over how genocide should be defined, lead also to disagreement on how many genocides actually occurred during the 20th Century.
Some say there was only one genocide in the last century - the Holocaust.
Other experts give a long list of what they consider cases of genocide, including the Soviet man-made famine of Ukraine (1932-33), the Indonesian invasion of East Timor (1975), and the Khmer Rouge killings in Cambodia in the 1970s.
Former Yugoslav leader Slobodan Milosevic is on trial in The Hague, charged with genocide in Bosnia from 1992-5.
However, some say there have been at least three genocides under the 1948 UN convention:
The mass killing of Armenians by Ottoman Turks between 1915-1920 - an accusation that the Turks deny
The Holocaust, during which more than six million Jews were killed
Rwanda, where an estimated 800,000 Tutsis and moderate Hutus died in the 1994 genocide
In the case of Bosnia, many believe that massacres occurred as part of a pattern of genocide, though some doubt that intent can be proved in the case of Mr Milosevic
The first case to put into practice the convention on genocide was that of Jean Paul Akayesu, the Hutu mayor of the Rwandan town of Taba at the time of the killings.
In a landmark ruling, a special international tribunal convicted him of genocide and crimes against humanity on 2 September 1998.
Twenty-one ringleaders of the Rwandan genocide have now been convicted by the International Criminal Tribunal for Rwanda.
Earlier this year, the war crimes tribunal for the former Yugoslavia widened the definition of what constitutes genocide.
General Radislav Krstic had appealed against his conviction for his role in the killing of more than 7,000 Muslim men and boys in Srebrenica in 1995.
But the court rejected his argument that the numbers were "too insignificant" to be genocide - a decision likely to set an international legal precedent.
On Darfur, Mr Powell says: "We can find the right label for it later, we have got to deal with it now."
But US envoy for war crimes Pierre Prosper has already started to compile a list of those associated with the Janjaweed Arab militia.
For the moment, these are threatened with sanctions but in the future, they may be charged with genocide, like those in Rwanda and the former Yugoslavia.
