Iraqi TV said medical teams were working on "stabilizing the president's condition after the brain stroke."
Initial reports from the president's office said Talabani, 79, was taken to the hospital Monday "due to fatigue and tiredness," Kuwaiti news service KUNA reported.
KUNA reported Talabani was under the care of a specialized medical team.
Talabani was elected president of Iraq in 2005, in the first free elections in the country in more than 50 years.
Talibani had heart surgery in the United States in 2008 and was treated for exhaustion and dehydration in Jordan the year before.