(CNN) -- Carrying blankets and bed sheets on their heads, thousands of refugees fleeing fighting in Chad's capital N'Djamena crossed a drought-stricken river to get to neighboring Cameroon Sunday, local officials and journalists said.

The violence in Chad has opened up a new conflict next to Sudan's wartorn Darfur region, where more than 200,000 people have died since early 2003 and 2.5 million people have been forced into refugee camps.

Government forces, under the direction of Chad's President Idriss Deby, continued a bloody battle for power in N'Djamena against the rebels, according to a French military spokesman.

Between 2,000 and 3,000 rebel soldiers armed with rifles roamed N'Djamena's streets in pickup trucks, the spokesman said.

The rebels entered the city on Saturday, local officials and journalists said. Read about causes of the violence

Chadian Ambassador to the United States Mahamoud Adam Bechir said the rebels were mercenaries supported by the government in neighboring Sudan. He said Sudan wanted to destabilize Chad's government. Watch why Sudan is being blamed »

Both the Sudanese and Chadian governments have previously accused one another of fomenting violence in the other's country by giving support to rebel groups.

On Sunday, the Chadian refugees flooded the Cameroon town of Kousseri, which lies just across the border from N'Djamena, according to Helene Caux, a spokeswoman for the United Nations High Commissioner for Refugees in Geneva.

She said authorities in Kousseri have put the number of Chadian refugees in the thousands. That was confirmed by Agnes Teile, a journalist for Cameroon television station Canal 2, who witnessed a steady stream of people -- mostly women and children -- spilling into Kousseri.

Some of the refugees were able to cross into Cameroon over a bridge, which was reopened earlier Sunday. Others had to wade through the river which was at low levels due to an ongoing drought.

Aid groups are struggling to reach the injured because of the ongoing fighting, according to the Chadian Red Cross which estimates about 200 have been wounded since Saturday.

Many of the injured are civilians caught in the crossfire, according to the aid group Doctors Without Borders -- known internationally by its French name, Medecins Sans Frontieres.

Some of those who fled to Cameroon also sustained injuries and are being treated by Cameroon's military and Red Cross, Teile said.

Cameroon authorities have warned the United Nations they could face problems providing aid if the refugee numbers swell, Caux said.

In response, UNHCR is sending three of its staff to Kousseri to help the relief effort.

It has also been difficult to get an accurate idea of the casualty count as a result of the ongoing fighting.

The U.N. Security Council also met Sunday for emergency talks on the fighting, with Secretary-General Ban Ki-moon calling for an immediate cease-fire.

"The Secretary-General is profoundly alarmed by the dangerous situation in Chad, particularly in light of the heavy fighting in several parts of the capital city, N'Djamena," according to a Sunday afternoon statement from Ban's office.

"He appeals to all countries in the region to respect the inviolability of international borders and to prevent any incursions from being launched from within their territory," the secretary-general's office said.

There are unconfirmed reports of bodies littering the streets in western N'Djamena. Watch CNN's Nic Robertson's report on latest violence »

"It is terrible in the west, a lot of bodies down. A lot of civilians," a hotel clerk at the Kempinski Hotel in eastern N'Djamena told CNN by phone.

The clerk said he had spoken to his brother who lives in the western part of the city. The brother said he had seen the bodies of men in military uniform lying in the street and people were afraid to move outside and were staying indoors.

The clerk said he heard gunfire coming from the area around the presidential palace Sunday. He said there was no fighting near the hotel but that on Saturday cars belonging to the rebels surrounded the government palace and his hotel.

Explainer Oil fueling ethnic violence in Chad

Some 1,600 French forces are helping evacuate hundreds of foreign nationals from N'Djamena; 400 foreign nationals left on Saturday and another 400 were slated to leave on Sunday.

Five evacuation centers were established around Chad's capital for foreign nationals to gather so they can be escorted by the French troops in armored vehicles to the airport, French Foreign Affairs spokesman Mathiew Ly said.

Also on Sunday, 103 U.N. staff were evacuated from the Chadian capital to the west African country of Gabon. A skeleton team of around 20 will remain in the city. Watch a discussion of possible solutions to conflicts in Africa »

The U.S. Embassy, in a statement Saturday, said it was evacuating selected employees and their families from N'Djamena, and asked that any American citizens who want to leave should contact the embassy.

The U.S. State Department on Sunday updated its travel advice, warning against any travel to the country.

The State Department issued a statement saying it had ordered the evacuation of all family members of Americans working for the embassy as well as all non-emergency American staff. It warned U.S. citizens still in N'Djamena to remain in safe locations indoors. E-mail to a friend

CNN's Cecile Pollet and Christabelle Fombu contributed to this report.

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