By Pascal Fletcher

BAMAKO, Mali (Reuters) - The United States is likely to eventually resume direct support for Mali's military, but only after full restoration of democracy through elections, the head of a visiting U.S. Congress delegation said on Monday.

Senator Christopher Coons, chairman of the Senate Foreign Relations subcommittee on Africa, was leading the first American congressional visit to the West African nation since France sent a military force there last month to halt an offensive by al Qaeda-allied insurgents.

The United States has been providing airlift and refueling support for the French-led operation involving hundreds of French and African troops that has driven the Islamist rebels from a string of northern Malian towns in the last five weeks.

Washington has also been sharing intelligence to back the operation, but has ruled out sending its own ground troops.

Coons, heading a four-member delegation from the U.S. Senate and House of Representatives, said both French and African military commanders were happy with the support that Washington was providing, but he indicated they might welcome more.

"There is the hope that there will be additional support from the United States in these and other areas," the Democratic Senator from Delaware told reporters in Bamako.

Asked if increased U.S. support for the military intervention could materialize, Coons said U.S. law prohibited direct assistance to Mali's armed forces because of the military coup there last year that toppled the elected government.

"After there is a full restoration of democracy, I would think it is likely that we will renew our direct support for the Malian military," he added.

French and African forces are hunting the Islamist insurgents who have retreated to Mali's remote northeast, and Malian interim President Dioncounda Traore has said presidential and parliamentary elections will be held in July.

Coons, whose delegation held talks with Traore, said the United States would strongly support inclusive elections.

"VERY REAL THREAT"

Coons said al Qaeda's North African wing AQIM and its allies in Mali and elsewhere posed a "very real threat" to Africa, the United States and the wider world and he said the United States wanted to be part of the response to this security challenge.

"We are committed to ensuring support of the United States in the ongoing fight against extremism," he added.

Before last year's coup in Mali - led by a U.S.-trained Malian army captain - the American military had been providing combat training to several Malian army battalions.

But this was quickly suspended after the coup, which plunged Mali into chaos and led to the occupation of its Saharan north by jihadists who hijacked a rebellion by Tuareg separatists.

Although the French-led offensive has driven the bulk of the Islamist forces northwards back up to the Algerian border, there are fears their fighters and sympathizers could strike back with reprisal attacks in Africa and elsewhere.

A top U.S. defense official last week called for international efforts to counter a "growing terrorist presence" of al Qaeda and its allies in Africa.

Coons was accompanied on the one-day visit by Georgia Republican Senator Johnny Isakson, and Congresswomen Karen Bass from California and Terri Sewell from Alabama, both Democrats.

(Reporting By Pascal Fletcher; Editing by Jason Webb)