Burkina Faso, Niger and Senegal on Saturday each pledged 500 troops for an African-led intervention force.
Ivory Coast's African integration minister Ally Coulibaly, speaking for the West African bloc ECOWAS, said the first soldiers could arrive as early as Sunday.
"We are not letting up the pressure," he added. "It is the reconquest of north Mali that has just begun."
On Saturday French troops arrived in the capital Bamako, flying in from bases in Ivory Coast and Chad, a Malian officer said. He refused to give details of their numbers or their mission.
Colonel Paul Geze, the French mission's commander, told Mali's ORTM television he hoped their mission would succeed "as quickly as possible, in the best conditions possible".
ORTM said the French contingent would be at full strength by Monday. It has been deployed in the capital to protect the 6,000-strong expatriate community.
Both France and Mali on Saturday hailed the success of their joint operation to push back an advance by the Islamists who control the north of the country.
Since taking power in the north last year, the Islamists have destroyed centuries-old Muslim mausoleums they see as heretical and imposed an extreme form of Islamic law including floggings, amputations and sometimes executions.
"Our foes have suffered heavy losses," French President Francois Hollande said, stressing that the French intervention had "only one goal, which is the fight against terrorism".
A statement late Saturday from Mali's interim president Dioncounda Traore said 11 of their soldiers had died and some 60 had been wounded in the fighting.
"They fell on the field of honour at Konna," the central town recaptured from the Islamists on Friday, it said.
French defence minister Jean-Yves Le Drian said French Mirage fighters had carried out a second day of air strikes Saturday to stop columns of Islamist fighters from driving south.
A French pilot carrying out air raids had been killed, he added. But the Islamists reportedly suffered heavy losses.
A Malian officer in the central town of Mopti, near the front line, said dozens, possibly as many as a hundred Islamists had been killed in Konna. Residents there described the bodies of men wearing Arab clothing and turbans.
Malian troops recaptured Konna Friday, just a day after it had fallen to the insurgents who had been threatening to continue their advance southward.
Human Rights Watch, citing reports from residents, said at least 10 civilians including three children had died in Konna.
Children forced by the Islamists to fight in their ranks had been wounded and possibly killed in the fighting, said HRW's Corinne Dufka.
The Islamists had conscripted the child soldiers in Mali's northeast region of Gao and captured others from neighbouring Niger, she added, calling for their immediate release.
France's intervention in Mali appears to have galvanised plans for a 3,300-strong, UN-approved African intervention force in Mali, which only a few days ago had not been expected to deploy until September.
As Western nations praised the French initiative, Britain offered technical support, though no troops on the ground.
Prime Minister David Cameron's office said that Britain would send two military transport planes to Mali to help ferry foreign troops and equipment.
In London Saturday around 60 Islamists including veiled women protested outside the French embassy, holding placards reading "French army, you will pay" and "Sharia is the only solution for Mali".
France tightens security at home
Hollande said he had ordered tighter security at home following the intervention in Mali, a former French colony.
France "has to take all necessary precautions" in the face of a terrorist threat including increased surveillance of public buildings and transport, he said.
European Commission President Jose Manuel Barroso on Saturday joined the chorus of Western support for the operation, praising the "courageous action by French troops".
But Russia's Africa envoy Mikhail Margelov said Africans alone should solve the continent's problems.
The Islamists seized northern Mali, a territory the size of France, in the wake of last year's March 22 coup which ousted democratically elected president Amadou Toumani Toure.
There were fears the north could become a haven for extremist groups. Some observers feared their recent advance south threatened the whole country.
Captain Amadou Sanogo, who briefly took power after the coup, on Saturday welcomed the French intervention.
Sanogo still plays a key role in the country's affairs despite having stepped aside in the face of international pressure. Previously, he had opposed foreign intervention in Mali.