Observers say Laghdaf, given his European diplomatic contacts, may have been appointed in a bid to lessen international condemnation of the coup.
The EU has said that the bloc would prefer Mauritania to return to the pre-coup situation and have the old government restored.
On Wednesday a majority of Mauritanian politicians from both the senate and the lower house declared their support for the coup which they said was carried out "in the interest of the Mauritanian people".
A statement, issed by the members, said the coup had been carried out "in the context of an acute political and institutional crisis" brought about by Abdallahi who "only listened to sycophants".
The politicians called on the world powers to support the coup leaders "in their objectives to preserve the stability of the country".
After ousting Abdallahi, Mauritania's first democratically elected president, in a coup on August 6, General Abdel Aziz formed the State Council comprised of 11 military officials to the government and promised to hold elections quickly.
The general began consulting political parties about the formation of a transitional government earlier this week.
Mauritania, a desert country which imports more than 70 per cent of its food needs, has been affected by the global food crisis.
In November last year, the northwestern African country faced food riots and the UN World Food Programme warned in March that the country faced a year of record hunger.
The country has also faced three attacks from groups linked to al-Qaeda which left seven people dead, including four French tourists.
The coup followed months of political tension and two recent government reshuffles.