BOGOTA, Jan 16 (Reuters) - Fighting between Colombia's two main guerrilla groups has forced around 2,000 people from their homes in a rare mass displacement near the border with Venezuela, the Red Cross and authorities said on Wednesday.

Violence from Colombia's 40-year conflict has eased under President Alvaro Uribe's U.S-backed security campaign, but guerrillas are still battling in rural and remote frontier areas such as Arauca province where the families fled.

"Due to armed hostilities and threats to the civilian population, more than 2,000 people have been displaced. The situation is critical," said a Red Cross spokesman in Bogota.

The aid agency has already sent basic assistance to more than 500 people who fled from rural areas to the town of Saravena. More aid will go to Arauquita and Pueblo Nuevo near the Venezuelan frontier, it said.

The Red Cross mentioned no armed groups. But the army said the fighting involved the FARC -- Revolutionary Armed Forces of Colombia -- and the smaller National Liberation Army or ELN, who have been battling for territory in places like Arauca.

Both groups have been weakened by Uribe's crackdown. The ELN is currently in fledgling peace talks with the government though talks in Havana have yet to yield concrete results.

The government says both rebel groups, which began in the 1960s fighting for socialism, have increasingly become involved in drug trafficking from the country's huge cocaine trade.

The United Nations says more than 3 million Colombians have been displaced by the conflict since the 1990s. But mass displacements of whole villages have become less common as the security situation improves.

(Reporting by Patrick Markey in Bogota; Editing by Cynthia Osterman)

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