"Turkey's conditions [of growing tension] make early elections necessary," the Milliyet newspaper quoted Sezer as saying in remarks to Devlet Bahceli, head of the nationalist National Movement Party.
"This is very important for calm in Turkey."
Opposition parties have also called for an early election, saying that parliament - last elected in November 2002 - needs a fresh mandate to select the next head of state.
Turkey's military, ultimate guardian of the secular order, is also believed to share this view.
Recep Tayyip Erdogan, the prime minister, denies any Islamist agenda and says that parliament will serve out its full five-year mandate, with an election to be held on schedule next November.
He has declined to say whether he will run for president.
Though parliament wields the greatest power in Turkey, the president is commander of the armed forces, has the right to appoint many key officials and can block legislation once.
Secularists fear that Erdogan would use the post to weaken Turkey's strict separation of state and religion, for example working to lift a ban on the Islamic headscarf in public offices and universities.
Sezer was also quoted as saying the threshold for entering parliament should be lowered to seven or eight per cent from the current 10 per cent to reflect the national will more accurately.
The centre-right AK Party, which has presided over strong economic growth and the launch of Turkey's European Union entry talks, has about two-thirds of the seats in the 550-seat parliament but won only 34 per cent of the vote in 2002.
It gained more seats because votes from parties unable to clear the 10 per cent threshold are redistributed.