He was rumored to have suffered a heart attack, but this was denied by his doctor and spokesman.
Wearing a light blue shirt and navy blue dressing gown, Talabani spoke in his normal tone of voice and smiled repeatedly during the interview.
"God willing, I will return safe and in a very good health to my country to continue my task with the Iraqi people," he said.
Talabani, a one-time leader of Kurdish guerillas who fought against Saddam Hussein, said his illness had perhaps been useful because it ensured that he received a full medical checkup.
He vowed to continue working for "a new, free, democratic, federal and united Iraq."
Doctor gives verdict
Yedgar Hishmat, Talabani's personal physician, said earlier on Thursday that the president was in "very good health and recovering rapidly."
"He is in a convalescence phase, but he still needs to finish his antibiotic course and is expected to leave the hospital within days" said Hishmat, who accompanied Talabani from Iraq.
Talabani is the first non-Arab to become president of a mostly Arab state.
However his position as president is mainly ceremonial and real power lies with Nuri al-Maliki, the prime minister, who is a Shia Arab.