Prime Minister Recep Tayyip Erdogan responded by calling for a constitutional amendment to allow the president to be elected by popular vote, rather than by the parliament. And he said new parliamentary elections could be held as early as June 24, instead of in November as scheduled.
The goal would be to elect a government with a fresh mandate and resolve a crisis that has seen the stock market plummet and the pro-secular military threaten to intervene.
"God willing, Turkey will go back to its track," Erdogan told reporters late Tuesday, referring to the economic and political stability that Turkey had enjoyed in recent years.
Earlier, Foreign Minister Abdullah Gul, the ruling Islamist party's presidential candidate, said he would not withdraw his candidacy despite Tuesday's setback from the Constitutional Court, a strongly secular body, and urged parliamentary elections "as soon as possible."
"What we need to cast off and get rid of these shadows is early elections," Gul said.
Erdogan said a new presidential vote would proceed in Parliament on Thursday.
"We will apply to Parliament starting tomorrow morning for early elections," he added. "The earliest possible date for elections is June 24 or July 1."
Erdogan's party appealed Thursday to parliament to hold the election on June 24.
At the heart of the conflict is a fear that Gul's party would use its control of both Parliament and the presidency to overcome opposition to moving Turkey toward Islamic rule. More than 700,000 pro-secular Turks demonstrated in Istanbul on Sunday, many of them women who believe political Islam would deprive them of personal freedoms and economic opportunities.
Secularists are deeply skeptical of the government despite its stated commitment to secularism, as well as reforms aimed at gaining membership to the European Union, because many ruling party members made their careers in Turkey's Islamist political movement. Erdogan once spent several months in jail after reciting an Islamic poem that prosecutors said had incited religious hatred.
The ruling party has advocated an eventual move toward a U.S.-style presidential system with a more powerful executive, adding to concerns about a president with an Islamist tilt.
In his remarks late Tuesday, Erdogan said he would push for a referendum if necessary on a constitutional amendment allowing the president to be elected by popular vote.
"If we cannot get the Parliament to choose a president, we will take this subject to the people and we will find a way to open presidential elections to our people," he said.
"With the decision of the Constitutional Court, the parliamentary democratic system has now been blocked," Erdogan added. "To get rid of this blockade and lift the rule of the minority over the majority, the only door to go to is the nation. Then, we are going to the nation."
Parliament, which since 2002 has been dominated by pro-Islamic politicians from Erdogan's ruling Justice and Development Party, elects the president in Turkey. In the first two rounds of voting, a candidate needs two-thirds of the lawmakers' votes to win, but by the third he needs only a simple majority.
The Constitutional Court ruled Tuesday that there were not enough legislators present during the first round of voting on Friday, and canceled the round. The opposition had boycotted the vote, depriving the ruling party of a quorum of two-thirds of lawmakers in the 550-seat Parliament.
"We've canceled the first round," court spokesman Hasim Kilic said. "Whether the Parliament will continue the vote or not, we can't know."
The Turkish stock market continued its slide Tuesday in reaction to the political upheaval, dropping 3.2 percent ahead of the Constitutional Court's decision later in the evening. The index had sunk 6.3 percent on Monday.
The bitter debate over the role of Islam in politics has exposed deep divisions in Turkey. Pro-secular groups say the ruling party, which came to power in 2002 with 34 percent of the vote, did not have a strong popular mandate even though an electoral quirk gave it 66 percent of the seats in Parliament.
The showdown has also led to fears that the military could intervene and push the elected government out of power.
Those concerns were heightened Friday when the army released a statement saying it was watching the process with concern and reminded Turks that the army was "the absolute defender of secularism" and would act to prove it if necessary.
Asked by reporters about the military statement, Erdogan said Tuesday that such debate should be avoided.
"This would weaken our country's institutions and would cause the country to lose blood," Erdogan said. "If the blood loss starts, than its price could be heavy for our nation as it happened in the past."
In 1997, the military pushed the pro-Islamic prime minister, Necmettin Erbakan, out of power, sending tanks into the streets in a message that any concessions on secularism would not be permitted. It staged three other coups between 1960 and 1980.
The founder of modern, secular Turkey, Mustafa Kemal Ataturk, was an army officer who established the republic in 1923 after the collapse of the Ottoman Empire, giving the vote to women, restricting Islamic dress and replacing the Arabic script with the Roman alphabet. Wearing an Islamic headscarf, as Gul's wife does, is illegal in government offices and schools.
But Islam remains a powerful and attractive alternative for many Turks in this predominantly Muslim nation of more than 70 million.