Turkey's ruling AK Party has asked parliament to approve an early general election amid deadlock over who should become the country's new president.
Mr Erdogan said that the people should choose their leader
The party proposed 24 June for the poll, which had been set for November.
The move comes after Turkey's constitutional court annulled last Friday's vote to elect a new president.
Secularist opposition parties boycotted the vote to prevent the ruling party candidate, Foreign Minister Abdullah Gul, from winning.
They accuse Mr Gul of having a hidden Islamist agenda and say that if he became president it would threaten Turkey's secular tradition.
The row over the presidency has exposed deep divisions. On Sunday, hundreds of thousands of people rallied in Istanbul in support of secularism.
The army has warned that it will not permit Turkey's secular traditions to be compromised, and financial markets in Turkey have also been hit by the crisis.
The decision to hold early elections must be debated by parliament and voted into law.
'Bullet at democracy'
On Tuesday, the constitutional court backed the opposition's argument that a quorum of two-thirds of the 550 lawmakers was not present for the first round of presidential voting.
2 May: Ruling party requests early elections
16 May: President Ahmet Necdet Sezer's term ends
24 June: Requested dates for early polls
4 November: Scheduled date for polls
A total of 361 lawmakers voted - 357 for Mr Gul - but 367 were needed to make a quorum, the court said.
Prime Minister Recep Tayyip Erdogan called the decision "a bullet aimed at democracy".
"The election for president in the parliament has been blocked," he told a party gathering on Wednesday.
"It has made it almost impossible for the parliament to elect a president in the future."
He has called for the constitution to be changed to allow the president to be elected by popular vote, rather than by parliament, and to allow the president to serve up to two five-year terms, instead of one seven-year term.
Mr Erdogan also pledged to move forward with a new round in the presidential vote - another vote is set for Thursday - but his candidate remains unlikely to secure the required two-thirds majority.
Analysts say Mr Erdogan's election move is an attempt to create a fresh mandate to end the crisis.
His party has presided over a period of strong economic growth and could fare well in general elections, analysts believe.
If Mr Gul does become president, he will be the first incumbent to have Islamist roots, and the first president whose wife wears an Islamic headscarf.
Both Mr Gul and Mr Erdogan deny there is any hidden Islamist agenda, and Mr Gul has pledged to adhere to the republic's secular principles if he were elected.
But critics fear that if the ruling party controls both the government and the presidency, it could then try to move Turkey towards Islamic rule and erode the separation of religion and state.