By Cheick Diouara

KIDAL, Mali (Reuters) - Around 1,000 troops from Chad led by the president's son advanced towards the mountains of northeast Mali on Thursday to join French search-and-destroy operations hunting Islamist jihadists.

A column of 100 Chadian armored vehicles, jeeps and supply trucks rolled out of Kidal, the Saharan town 1,200 km (750 miles) northeast of the capital Bamako. From Kidal, French and Chadian forces backed by French warplanes are striking against Islamist rebel hideouts in the Adrar des Ifoghas mountain range straddling the border with Algeria.

President Idriss Deby's son, General Mahamat Idriss Deby Itno, commanded the Chadian column. He told Reuters its mission was to "fight terrorism, and eradicate it from the region", a reference to the al Qaeda-allied fighters in the mountains who are being bombarded almost daily by French aircraft.

More than 2,500 troops from Chad and Niger are assisting 4,000 French soldiers in the second phase of Paris' four-week-old intervention against al Qaeda and its allies in Mali. This is supported by Africa, the United States and Europe as a strike against radical jihadists threatening international attacks.

France's Operation Serval has retaken the main urban areas of Mali's north, including Timbuktu and Gao, and is now pursuing the retreating jihadists into the remote northeast. Malian troops are moving up behind to secure the recaptured locations.

Malian Defense Minister General Yamoussa Camara told Reuters the Malian army intended to follow the French and Chadians right up to Tessalit close to the Algerian border.

"That is going to take some time. The enemy's offensive has been broken, they've lost a lot of equipment, but there are pockets of resistance scattered across the country," he said.

This echoed statements by French leaders who say the Islamists have suffered "hundreds" of casualties but warn the Mali campaign is not yet over. France has said it wants to start pulling troops out of its former colony in March and would like to see a U.N. peacekeeping force deployed there by April.

Pro-autonomy Tuareg MNLA fighters, whose revolt last year defeated Mali's army and seized the north before being hijacked by Islamist radicals, have said they are controlling Kidal and other northeast towns abandoned by the fleeing Islamist rebels.

Tuareg desert nomads, offering local knowledge as guides, have said they will help the French and Chadians hunt down the al Qaeda-allied insurgents in the desert and mountains.

But this has created a potentially sensitive situation as Mali's government and army insist on restoring Bamako's sovereignty over every corner of Mali, including the vast and empty desert zone which the Tuaregs claim as their homeland.

"It is out of the question that we would abandon any place to the MNLA," Defence Minister Camara said.

U.S. WANTS "DEMOCRATIC SOLUTION"

In the absence of Malian government troops in Kidal for the moment, Tuareg MNLA fighters in their own 4x4 vehicles were accompanying the Chadians as they headed north towards the mountains, a Reuters reporter in Kidal said.

France has urged Mali's government to open a dialogue with the Tuaregs to settle grievances over alleged neglect and mistreatment that have triggered a series of Saharan rebellions by the "blue men of the desert" - so called because of their indigo blue turbans and robes - since Mali's 1961 independence.

The United States added its voice on Thursday to this call for talks with the Tuaregs, a political settlement and elections to restore democratic rule in Mali. The Malian military that staged a coup in March last year retains influence.

"A military solution without a democratic solution is an imperfect solution," U.S. Assistant Secretary of State for African Affairs Johnnie Carson said in a conference call with reporters.

He also called for negotiations between Mali's government and "moderate Tuareg, those that renounce violence".

"Many have longstanding political grievances, legitimate and longstanding. They must be dealt with."

Carson said Mali, the United States and their allies should remain focused on eliminating al Qaeda and its followers not only from Mali, but from the region as a whole.

Meeting in Cairo, leaders of Muslim nations declared support for the unity and territorial integrity of Mali and condemned terrorism in the west African state, but made no mention of the French military intervention.

U.S. officials say al Qaeda's North African wing AQIM, part of the Islamist rebel alliance that had occupied northern Mali, has links with other radical Islamist groups in Africa, such as al Shabaab in Somalia and Boko Haram in Nigeria.

Washington and the European Union are supporting the French operation in Mali with airlift, logistical and intelligence support. U.S. unmanned surveillance drones are being sent to Mali's Sahel neighbor Niger to fly from there into the Sahara.

Carson declined to comment on the deployment of the drones.

(Additional reporting by Tiemoko Diallo in Bamako, Richard Lough in Nairobi, Richard Valdmanis in Dakar, Paul Taylor in Cairo; Writing by Pascal Fletcher; Editing by Robert Woodward)