He said an "atmosphere of stability and tranquility" was essential.
Mr Erdogan's ruling Islamist-rooted AK party has put forward Foreign Minister Abdullah Gul for president. But the army has hinted it may block him.
Last week Mr Gul was backed in a vote in parliament, but the constitutional court has been asked to annul the vote.
It says it hopes to rule on the petition before the next round of the vote is due to take place on Wednesday.
In
As many as one million people marched through
They were supporters of
Markets fall
The president is traditionally a key upholder of the country's separation of religion and state.
Mr Gul has Islamist roots, and his wife wears the headscarf, which is very controversial in
He says there is no question of him withdrawing from the presidential election, and promises to respect the secular tradition.
A somber-looking Mr Erdogan stressed his government's achievements, including its economic record, since coming to power in 2002.
"Even four-and-a-half years ago, this country was riven by serious problems, which thank goodness have been overcome one by one," said Mr Erdogan.
He said the average growth rate from 2003 to 2006 was 7.3%, while per capita income had almost doubled.
"Unity, togetherness, solidarity, these are the things we need most. We can overcome many problems so long as we treat each other with love," Mr Erdogan said, though he did not make any direct reference to the current crisis.
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The first round of the election in parliament ended in disarray on Friday amid a dispute about the number of deputies present for the vote.
The secularist Republican People's Party (CHP), which boycotted Friday's vote, claimed that although a majority backed Mr Gul, a quorum of MPs had not been obtained. It referred the complaint to the constitutional court.
If the court upholds the CHP position and cancels the presidential election, the ruling would trigger an early general election.
'Test case'
Some opponents fear Mr Gul has a hidden Islamic agenda, and the army has made clear it does not want him in the presidential palace, says the BBC's Sarah Rainsford in
The government has sharply criticized the army's threat to intervene in politics, saying the military must remain under civilian control.
The army has carried out three coups in the last 50 years - in 1960, 1971 and 1980 - and in 1997 it intervened to force
EU Enlargement Commissioner Olli Rehn has said the row is "a clear test case whether the Turkish armed forces respect democratic secularization and democratic values".
Photo caption
Turkish secularist marchers in