Iraqi President Jalal Talabani will soon be flown to Germany for further treatment, officials say, two days after he reportedly suffered a stroke.
Earlier, the deputy health minister and the director of the hospital where Mr Talabani is being treated both said his condition was stable and improving.
Hospital and government sources had said on Tuesday that he was in a coma.
A veteran of the Kurdish guerrilla movement, Mr Talabani, 79, is Iraq's first president from the ethnic group.
He has struggled with his health in recent years and often been treated abroad. He underwent heart surgery in the US in 2008.
Mr Talabani was apparently rushed to the Baghdad Medical City on Monday evening, although no announcement was made until Tuesday morning, when officials said he had suffered a "health emergency".
A statement from the president's office said his bodily functions were "normal" and that his condition was "stable". The emergency was caused by hardening of the arteries, it added.
But officials conceded in private that his condition was more serious.
First, state television reported that Mr Talabani had suffered a stroke. Then, hospital, government and Kurdish sources said he was in a coma.
On Wednesday, the director of Baghdad Medical City that the president was getting better, but offered no details about the severity of the illness.
"Tests showed the stability and improvement of his excellency's health condition," Dr Hani Moussa Badr told a news conference.
Deputy Health Minister Issam Namiq said Mr Talabani's condition was "stable" and that there had been "an improvement".
Mr Namiq said both Iran and Germany had sent medical teams to assist in Mr Talabani's treatment, and that a British team was due to arrive soon.
Later, senior Kurdish officials said the German doctors had recommended that the president be flown abroad for further treatment, possibly as early as Thursday. Neighbouring Turkey has offered to provide an air ambulance.
"Most likely he will be transferred within 24 hours," Najmaldin Karim, the governor of Iraq's Kirkuk city who is also part of the president's medical team, told the Reuters news agency.
It was also confirmed by the head of the president's media office, Barazan Sheikh Othman.
"Most probably the president will be taken tomorrow, or at maximum the day after tomorrow, to Germany to complete his treatment," Mr Othman told the Associated Press. "The president's medical situation has improved and he has passed the dangerous stage."
Mr Talabani's illness comes at a time of heightened political tensions between Iraq's Arab-led central government and the semi-autonomous Kurdish region in the north.
In recent weeks, he has been mediating in the dispute triggered by the government's attempt to take greater control of security in oil-rich territory around the city of Kirkuk, which is claimed by both Arabs and Kurds. Kurdish forces have been deployed in the region since 2003.
A deal brokered by Mr Talabani called on both sides to eventually withdraw troops from the contested areas, though no deadline was set.
The president, whose powers are limited, is seen as a unifying figure who has helped prevent the disintegration of Iraq's fragile national unity government, which includes Shia and Sunni Arabs as well as Kurds.
On Monday, Mr Talabani met Prime Minister Nouri Maliki to discuss the political problems. Afterwards, the president's office said they had both stressed the need for calm and transparent dialogue, as well as "working according to the spirit of the constitution and the national agreements".
Mr Maliki has visited the president in hospital since his admission.
According to Iraq's constitution, one of the two vice-presidents assumes the presidency temporarily if it becomes vacant. A new president would then be elected by parliament within 30 days.