Mr Guterres “reiterates his concern over the health and safety of the President and his family and once again calls for his immediate, unconditional release and his reinstatement as head of state,” his spokesman said on Wednesday.
In text messages to a friend, Mr Bazoum said he was being held in isolation and forced to eat dry rice and pasta, CNN reported.
The President said he had been “deprived of all human contact since Friday”, with no one supplying him with food or medicine.
He was confined to his presidential residence on July 26, two days before Gen Abdourahmane Tchiani, commander of the presidential guard, declared himself ruler.
The coup has left the impoverished nation even more isolated, with foreign aid slashed and regional powers threatening to put troops on the ground.
The US has also said it is “greatly worried” about Mr Bazoum's health and the safety of his family, with the president reported to be held with no water or electricity.
Secretary of State Antony Blinken has spoken with the detained leader over the phone, Washington confirmed on Wednesday, following unsuccessful attempts from State Department officials to meet him during an unannounced visit on Monday.
“As time goes on, as he's held in isolation, it's a situation that is of growing concern to us,” said spokesman Matthew Miller.
Representatives of the 15-member Ecowas bloc are expected to favour diplomacy over troops on the ground – which regional chiefs have described as a “last resort” but not ruled out completely.
The bloc has already met in Nigeria, which is leading dialogue on Niger, to discuss the crisis, initially issuing sanctions following the coup after their deadline to reinstate President Bazoum expired on Sunday.
Niger's junta met with Nigerian envoys on Wednesday but accused France of allegedly violating its airspace and releasing jailed militants, claims dismissed by Paris as “unfounded.”
France, a traditional ally of Niger, has worked closely with the government on counterterror efforts in the Sahel alongside several other western powers.