Although ruling AK party candidate Abdullah Gul won the poll a boycott by the opposition meant the court declared not enough of the country's legislators backed him, judges ruled.
Now prime minister Tayyip Erdogan wants parliament to call early elections in order to break the deadlock.
"The essential problem is to manage to stay united, preserving our differences. Rights and freedoms are necessary for everybody," the AFP news agency quoted him as saying.
He insisted that the AK party was not committed to reintroducing an Islamist agenda into the government, but called for constitutional changes which would tie the presidential election more closely to the popular vote.
The Turkish parliament will now vote on whether or not to dissolve itself and hold general elections on June 24th.
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