However, a doctor treating Mr Bhiri in detention told AFP he was in a "stable condition".
Mr Bhiri and former interior ministry official Fathi Baldi of the Ennahdha party were arrested by plainclothes police officers on December 31 and later accused of possible "terrorism" offences. Neither have been formally charged.
Mr Bhiri, 63, who suffers from diabetes, high blood pressure and a heart condition, has been on hunger strike since he was detained.
Ennahdha said on Facebook Mr Bhiri's "state of health has reached a very dangerous stage and he is close to death".
It said it held the authorities "fully responsible" for his life.
But a doctor at the hospital where he is being held in Bizerte, north of Tunis, told AFP "there has been no development in his condition, which remains stable".
Ennahdha has played a central role in Tunisian politics since the revolution that overthrew dictator Zine El Abidine Ben Ali in 2011.
But it has since become a principal target of President Kais Saied, who last July sacked the government and froze the Ennahdha-dominated parliament, later moving to rule by decree.
While some Tunisians, tired of a system seen as corrupt, have backed Mr Saied's moves, his opponents and civil society groups have voiced fears of a slide back to the authoritarianism of Ben Ali.
The UN rights commission and Human Rights Watch have both called for Mr Bhiri and Mr Baldi to either be charged or released.
As well as staging a hunger strike, Mr Bhiri had initially refused medicines for his existing conditions, but later acquiesced, his doctors said.
Tunisia's anti-torture commission, the INPT, which had visited Mr Bhiri in hospital on Sunday, said it was planning another visit.
An INPT source told AFP Mr Baldi had been allowed visits by the commission's officials and by family members, but said neither men had been allowed access to a lawyer.
The source urged authorities to respect the men's "right to a defence and right to a legal procedure transparently monitored by a judge".