The court upheld an appeal from the secularist opposition that wants to stop the ruling AK Party's presidential candidate, Islamist-leaning Foreign Minister Abdullah Gul, from becoming head of state.
The court ruled there were not enough lawmakers present in the first-round vote for a necessary two-thirds quorum in parliament. The ruling opens the way for possible early general elections.
Government spokesman Cemil Cicek said shortly after today's ruling that parliament will try to gather the required attendance of parliamentarians for another presidential vote on May 2, but the vote was immediately postponed.
Cicek also said the government is willing to hold early general elections, providing parliament agrees to lower the age requirement for candidates.
The opposition has expressed concern that Gul may try to implement an Islamist agenda.
The military had threatened to intervene to preserve Turkey's secular traditions.
In a televised address on April 30, Prime Minister Recep Tayyip Erdogan appealed for national unity.
"Unity, togetherness, solidarity, these are the things we need most," Erdogan said. "We have to reach to sublime kindness together, this is the most important gain for us. We can overcome many problems so long as we treat each other with love. Turkey needs this unity, solidarity and love, free of prejudice."
Meanwhile, Turkish police detained dozens of people taking part in May Day rallies in Istanbul today.
Most of the up to 100 detentions were made when participants in one of two major rallies in the city tried to march on the central Taksim Square in defiance of a ban by city authorities.
Police had blocked roads to prevent people from reaching the site to commemorate a May Day rally there 30 years ago, when unidentified gunmen opened fire on demonstrators, sparking a stampede that left more than 30 people dead.
(AFP, AP, Reuters)