Should Talabani be incapacitated, Iraq would lose an influential negotiator who often stepped in to ease tensions in the fragile power-sharing government and between the central government and the country's autonomous Kurdistan region.
Talabani's office said he was admitted to a Baghdad hospital on Monday night and the 79-year-old president was in stable condition under intensive medical supervision after receiving treatment for blocked arteries.
"He was transferred to hospital late last night after suffering a stroke," a senior Kurdish official said.
Talabani had been suffering from ill health this year and received medical treatment overseas several times in the last two years.
Prime Minister Nuri al-Maliki visited the president at the Baghdad hospital on Tuesday.
According to Iraq's constitution, the parliament should elect a new president if the post becomes vacant. Under Iraq's power-sharing deal the presidency should go to a Kurd while two deputy president positions are shared by a Sunni Muslim and a Shi'ite Muslim.
Talabani recently helped ease a military stand-off between Maliki's central government and the autonomous Kurdistan president, Masoud Barzani, in a dispute over oil-field rights and internal boundaries. Both regions sent troops to reinforce positions along their internal frontier.
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.