Haydar al-Zamili, the local health authority's spokesperson, said early Tuesday 52 bodies were retrieved and another 22 people were wounded in the latest toll, after the fire had "ripped through the Covid isolation ward".
"The victims died of burns and the search is continuing," he added, noting that there were fears people could still be trapped inside the building.
The ward had space for 70 beds.
The deadly hospital blaze is the second such fire in Iraq in three months.
Outside the hospital, dozens of young demonstrators protested.
"The (political) parties have burned us," they shouted in unison.
The fire also prompted furious calls on social media for the resignation of top officials.
Local authorities imposed a state of emergency in Dhi Qar governorate, of which Nasiriyah is the capital, and ordered doctors on leave to help treat the injured.
'Failure to protect lives'
Iraqi prime minister Mustafa al-Kadhemi held an emergency meeting with ministers and security heads to "find out the causes" of the fire, his office tweeted Tuesday.
Dhi Qar's health chief and the hospital's head were detained and questioned by police, his office said.
Kadhemi also dispatched emergency medical aid to the southern governorate.
"The catastrophe of Al-Hussein Hospital is clear proof of the failure to protect the lives of Iraqis, and it is time to put an end to this," Mohamed al-Halbousi, Iraq's Parliament Speaker, wrote on Twitter.
Iraq's interior ministry said on Facebook that the fire tore through temporary structures erected next to the main building, but did not specify the cause.
Videos shared online showed thick clouds of smoke billowing from the Al Hussein hospital.
In April, a fire at a Baghdad Covid-19 hospital killed 82 and injured 110, sparked by the explosion of badly stored oxygen cylinders.
Many of the victims in the April fire were on respirators and were burned or suffocated in the resulting inferno that spread rapidly through the hospital, where dozens of relatives were visiting patients in the intensive care unit.
The April fire led to widespread anger, resulting in the suspension and subsequent resignation of then health minister Hassan al-Tamimi.
Iraq -- where the oil-reliant economy is still recovering from decades of war and insurgency, and where many people live in poverty -- has recorded over 1.4 million coronavirus cases and more than 17,000 deaths.
Much of the country's health infrastructure is dilapidated and investment in public services is limited by endemic corruption.
Since the coronavirus vaccine rollout began in March, Iraqi health authorities have fully inoculated only around one percent of the country's roughly 40 million people.
Earlier on Monday, a minor fire broke out at the health ministry's headquarters in Baghdad, but it was quickly contained with no fatalities recorded.