Asked to indicate which party they would vote for if elections were held today, 43.4 per cent listed the AKP, while the main pro-secular force in parliament, the Republican people's party (CHP), received backing from just 18.1 per cent.
The AKP won the last elections in July 2007 with 47 per cent of the vote and the next poll would not normally be due until 2011.
The country's chief prosecutor has said that the AKP plans to replace the secular system with a religious regime. Should the constitutional court heed the prosecutor's demand, it will be the first time that it has outlawed a governing party.
However, the survey, conducted over two days in the middle of June from a sample of 1,195 people, confirmed the belief that even if the AKP is banned by the court, its successor would win early elections.
As well as banning the AKP, the prosecutor is seeking a five-year ban on the political activities of some 71 figures, including Abdullah Gul, the Turkish president and former leader of the AKP, and Recep Tayyip Erdogan, the prime minister.
The AKP has rejected the allegations, saying it is the target of a politically-motivated attack and frequently reaffirming its commitment to secularism.