Algerian diplomats were kidnapped by al-Qaida allies who seized territory in northern Mali following a coup in Bamako in 2012.
Algerian Foreign Minister Ramtane Lamamra was quoted by the official Algeria Press Service as saying the government deployed "huge efforts" to secure their release.
The Foreign Ministry last month extended a message of congratulations to new Malian President Ibrahim Boubacar Keita. The Algerian government said it had a "deep ... and strong relationship with Mali."
Mali is struggling to ensure national unity following a 2012 coup. The interim government called for military support from former colonial power France to help fight al-Qaida and nomadic fighters who took control in northern Mali after the coup.
The BBC reported Tuesday a bridge in the city of Gao was bombed by militants. It came a day after the city was shelled by forces suspected of being aligned with those who seized northern turf after the coup.