Gul stands firm..........from bbc
 The military said it will act to defend secularism in Turkey |
Mr Gul failed to win election in a first round vote in parliament as opposition MPs boycotted the vote and challenged its validity in court.
An army statement on Friday accused the government of tolerating radical Islam and vowed to defend secularism.
Supporters of the secular system are holding a major rally in Istanbul.
Two weeks ago a similar rally in Ankara attracted hundreds of thousands of secular supporters.
Sunday's "Republican Meeting", planned by dozens of non-governmental organisations, is taking place in Caglayan Square in Istanbul.
'Test case'
On Saturday, Cemil Cicek, spokesman for the ruling party, the Islamist-rooted AK (Justice and Development), responded to the unusually forthright army statement.
The military, which led coups in the past, said it was concerned by the party's choice of presidential candidate.
Mr Cicek said any intervention was "inconceivable in a democratic state".
"The chief of the general staff is answerable to the prime minister," said Mr Cicek, who is also justice minister.
The European Union warned the army not to interfere in politics, saying the controversy was a test case for the military to respect democracy.
The BBC's Sarah Rainsford says the army is sending a signal that it will not accept Mr Gul's candidacy.
Mr Cicek told reporters that the government had the "primary duty in protecting the basic tenets of the state".
Prime Minister Tayyip Erdogan has been meeting his cabinet to discuss the situation.
According to Mr Cicek, the prime minister had a "useful and productive" telephone conversation with army chief Gen Yasar Buyukanit on Saturday afternoon.
Turkey is an EU candidate but entry negotiations have been partially frozen because of a dispute over Cyprus, and the EU is also concerned that Turkey's commitment to political reform is weakening.
EU Enlargement Commissioner Olli Rehn said the row was "a clear test case whether the Turkish armed forces respect democratic secularization and democratic values".
History of coups
Our correspondent in Istanbul says the army statement late on Friday night caused a real stir in Turkey.
Many also believe that it is also a message to the judges in the constitutional court to declare the vote invalid and dissolve parliament, she adds.
The army has carried out three coups in the last 50 years - in 1960, 1971 and 1980 - and in 1997 it intervened to force Turkey's first Islamist Prime Minister, Necmettin Erbakan, from power.
The AK is an offshoot of Mr Erbakan's Welfare Party, which was banned in 1998.
The secularist Republican People's Party (CHP), which boycotted Friday's vote, said it would challenge the election in court because a quorum of MPs had not been obtained - a charge the AK denies.
A second round of voting is due on Wednesday and the court has said it will try to rule on the appeal before the vote.
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