The official did not give further details on the whereabouts of the plane or the cause of the accident, Reuters reported.
Spain's foreign ministry told The Local they were unable to confirm reports the plane had crashed.
However, France's foreign minister Laurent Fabius conceded at a later press conference the plane has "probably" crashed.
"Despite intensive searches, no trace of the plane has been found as we speak," he said in Paris.
"The plane has probably crashed. The searches are focusing at this stage on a vast strip of Malian territory around the region of Gao," in the north of the west African nation, he said.
Reports in the French press claim the McDonnell Douglas MD-83 plane came down near the town of Tilemsi, in the Gao region of northern Mali. Those reports cited local Algerian and Malian sources.
Air traffic controllers lost track of the plane at 1.55am GMT on Thursday morning, some 50 minutes after take off.
Algeria's Prime Minister has confirmed contact was lost with the plane when it was over the politically sensitive region of Gao in northern Mali.
"The plane was not far from the Algerian frontier when the crew was asked to make a detour because of poor visibility and to prevent the risk of collision with another aircraft on the Algiers–Bamako route," a source with airline Air Algérie told news agency AFP.
"Contact was lost after the change of course."
Reuters quoted a diplomat in Bamako, Mali's capital, saying there had been serious sand storms in the area overnight.
Satellite image showing storms over Air Algerie route last night: pic.twitter.com/Kkf0R5UiF2— Alistair Bunkall (@AliBunkallSKY) July 24, 2014
There were 110 passengers and six crew members on board the plane, Swiftair initially reported.
Air Algérie has added three more passengers, taking the total number on board to 119.
France's Le Parisien newspaper quoted an Air Algérie official as saying the passenger list included 6 Algerians, 51 French, 24 from Burkina Faso, one Malian, one Belgian, two from Luxembourg, five Canadians, one Cameroonian, four Germans, one Nigerian, eight Lebanese, one Egyptien, one Ukrainian, one Swiss, and six or seven members of the Spanish crew.
Many passengers were transiting to destinations including Dubai, Paris, Montreal, Cairo and Beirut, according to French media outlet France Info.
Swiftair said earlier there were two Spanish pilots and four Spanish crew members on the flight.
Spanish authorities have set up an emergency number for relatives at +34 900 264 270.
The Spanish public works ministry has set up an emergency committee to deal with the crisis, while the foreign affairs ministry is mobilizing its diplomatic staff in West Africa.
Swiftair is a Madrid-based aviation company which offers cargo and passenger flights in Europe, North Africa and the Middle East. Founded in 1986, they currently have a fleet of 45 planes.
They operate charter flights for airlines including Iberia, Vueling and Air Europa.
They carried just under 20,000 passenger in Africa in 2013, according to Spain's Aena airports authority, in figures cited by El País newspaper.
The Air Algerie jet leased from the firm that went missing on Thursday was checked "two or three days ago" and was "in good condition", France's aviation watchdog said.
The Swiftair statement
A senior French official on Thursday said it was unlikely that rebel fighters in Mali had shot down the plane as they did not have the weaponry, the Huffington Post reported.
Last year, France sent troops to Mali to free it from the grip of Islamists after rebels captured large swathes of the desert country's territory.
Despite international military intervention still under way, the situation remains unstable in northern Mali, which was seized by jihadist groups for several months in 2012.
On July 17th, the Bamako government and armed groups from northern Mali launched tough talks in Algiers aimed at securing an elusive peace deal, and with parts of the country still mired in conflict.