Gen Abdelaziz says they are holding the president to maintain calm
The African Union (AU) is to suspend Mauritania's membership of the group following a coup which overthrew the democratically elected president.
The chair of the AU said that the suspension would last until a constitutional government was restored.
Renegade soldiers detained President Sidi Ould Cheikh Abdallahi on Wednesday after he tried to sack army officers.
The coup has been widely condemned by the international community and the US has suspended all non-humanitarian aid.
"The coup is a serious setback for Mauritanians because it has robbed the people of their basic right to freely elect leaders of their own choice," said Tanzania's Foreign Minister Bernard Membe, who holds the AU's rotating presidency.
No poll date
President Sidi Ould Cheikh Abdallahi is being held along with the country's prime minister in an undisclosed location.
Gen Muhammad Ould Abdelaziz, who led the military coup, has pledged to safeguard democracy in the country but has, as yet, set no date for an election.
A representative from the Arab League said he held talks with Gen Abdelaziz and was assured that democracy would be restored.
"We got guarantees that the parliament, the democratic institutions, the political parties and freedom will continue to exist," Assistant Secretary General Ahmed bin Heli told reporters.
However, in remarks published on Saturday, Gen Abdelaziz said they would continue to detain the president to avoid any escalation.
"We will not release the deposed president at the time being for security reasons. We are now trying to make calm prevail," he is quoted as telling the London-based daily Asharq al-Awsat.
The US has withheld more than $20m (£10m) in non-humanitarian aid to the country following the coup.
The funds include $15m (£7.5m) in military-to-military co-operation, more than $4m (£2m) in peacekeeping training, and more than $3m (£1.5m) in development assistance.
Mr Abdallahi became Mauritania's first democratically elected leader in 2007 after a coup two years earlier, also instigated by Gen Abdelaziz.
It was the first free and fair poll in more than two decades in the country.