Two Armoured Personnel Carriers (APC) of the French Army patrol a rural area during the Bourgou IV operation in northern Burkina Faso. AFP
A unit in Tin-Akoff in Oudalan province near the border with Mali "came under violent attack" on Monday evening, a source said, giving a toll of "about 15 dead" with others still missing.
The army mounted a counter-attack with air support, "neutralising... dozens of terrorists," the source added.
A second source in the security forces confirmed the assault and put the toll at 19 soldiers dead and "dozens of missing."
The bloodshed came as the Sahel nation reeled from a deadly ambush last Friday near Deou, also in Oudalan province.
Fifty-one soldiers died and 160 jihadists were killed in that action and the aftermath, according to army figures.
Jihadist insurgents in Mali began launching cross-border incursions on the landlocked Sahel state more than seven years ago.
Since then, than 10,000 civilians, police and troops have died, according to NGO estimates, and more than two million people have fled their homes.
Around 40 percent of the nation's territory lies outside the government's control.
Anger within the military at failures to turn the tide sparked two coups last year.
Hours before news broke of the latest attack, political parties and civil groups displayed their support for the ruling junta.
"In these difficult times, I urge the Burkinabe people to cultivate a spirit of national unity and support the transitional authorities in their resolve to restore our territorial integrity," said Zephirin Diabre of the Union for Progress and Change (UPC).
Junta leader Captain Ibrahim Traore acknowledged the fight against jihadism was "strewn with pitfalls" but said the authorities remained "determined" to triumph.
Friday's attack was the deadliest among the security forces since Traore, 34, took power in late September, vowing to recover territory captured by the jihadists.
But attacks have escalated sharply in recent weeks -- since the start of the year, more than 200 people have died, according to an AFP toll.
Political commentator Harouna Traore asked why the armed forces seemed to be so vulnerable.
"Why are patrols being carried out without aerial surveillance? Today, we have drones, reconnaissance aircraft, which should mean we no longer run into ambushes," he said.
Burkina Faso's junta, like its counterpart in Mali, has fallen out with France, the country's traditional ally.
France is pulling out its troops -- a special forces unit of around 400 men based near the capital Ouagadougou.