Without Talabani, Iraq would lose an influential peace-maker who often eased tensions in the fragile power-sharing government and negotiated in the growing rift over oil between Baghdad and the OPEC member country's autonomous Kurdistan region.
Reports on his medical condition varied. Three government sources said he was in critical condition, but his office said the 79-year-old president was stable under intensive medical supervision after receiving treatment for blocked arteries.
"President Talabani has suffered a light stroke. His condition is stable now and doctors are closely monitoring him and if they decide he should be transferred outside then he'll go," veteran Kurdish politician Mahmoud Othman, a close Talabani associate who was in the Baghdad hospital.
Talabani had been suffering from ill health for much of this year and received medical treatment overseas several times in the last two years.
Prime Minister Nuri al-Maliki visited the hospital earlier on Tuesday.
TOUGH TIMES AHEAD?
Under Iraq's constitution, the parliament should elect a new president if the post becomes vacant and Iraq's power-sharing deal calls for the presidency to go to a Kurd while two vice presidents are shared by a Sunni Muslim and a Shi'ite Muslim.
Political analysts said former Kurdistan prime minister Barham Salih is favored candidate to replace Talabani should the president be incapacitated.
But his exit from Iraqi politics would come at a sensitive time and any succession would be complicated, a year after the last American troops left the country.
"He is the most moderate among Iraqi politicians and the most able to defuse political shocks. I do not think anyone will be able to fill his position as a president and as a politician," Iraqi analyst Ibrahim al-Sumaidaie said.
Iraq law would see one of the vice presidents take over Talabani's duties before the parliamentary vote. But Iraq's Sunni Vice President, Tareq al-Hashemi, is outside the country after he fled to escape charges he ran death squads. He has been sentenced to death in absentia.
Any parliament vote would also be complex, with Maliki locked in a struggle with Sunni, Kurdish and some Shi'ite rivals in the power-sharing government. Talabani was crucial in helping the Shi'ite leader survive a no-confidence motion directed against him earlier this year.
Talabani also recently helped ease a military stand-off between Maliki's central government and the president of autonomous Kurdistan, Masoud Barzani, in their long-running dispute over oil-field rights and internal boundaries.
That situation remains sensitive after the two sides sent troops to reinforce positions along their internal frontier.
Kurdish forces said on Tuesday they fired on an Iraqi military helicopter near Sikanyan town just north of the ethnically mixed city of Kirkuk, to keep the aircraft from taking surveillance pictures of their military positions.
There were no casualties in the incident, authorities said.
A veteran of the Kurdish guerrilla movement, Talabani survived wars, exile and infighting in northern Iraq to become the country's first Kurdish president a few years after the 2003 invasion that toppled Saddam Hussein.
(Additional reporting by Raheem Salman, Aseel Kami and Isabel Coles; Writing by Patrick Markey; Editing by Andrew Roche)