"The evidence is crystal clear. We know the terrorist cult responsible for vicious attacks against us and the Turkish people," Yildirim said in an interview with the Wall Street Journal.
"We are heartbroken at the way that the U.S. has treated this matter. We simply cannot understand why the U.S. just can’t hand over this individual."
Yildirim added that the U.S.-Turkish strategic alliance's strength must outweigh the procedural matters.
The premier also said Turkish investigators' testimony compiled from the coup plotters must be considered credible.
Following the July 15 coup attempt in Turkey, where more than 240 people were martyred, Turkey said U.S.-based preacher Gulen masterminded it and regards him as the head of FETO, or Fetullah Terrorist Organization.
Though Turkey sent an official extradition request last week, the U.S. insists that needs to see evidence to send Gulen back to Turkey.
Yildirim stressed that the U.S. kept asking for documents but the martyrs, who were bombed from jets and run over by tanks, were already enough as proof.
"The evidence is clear. We have testimony by suspected members of the coup that they took orders from this person," he said.
The prime minister said the putsch attempt shook the nation as the 9/11 attacks did the U.S., and all current ongoing investigations were conducted in accordance with legal and constitutional parameters.
Yildirim also denied claims that detainees are being tortured or mistreated.
Although Turkey had previously opened court cases against Gulen and his organization before the failed coup, Yildirim says that the government was not "firm enough" in its prosecution.
According to Turkish Justice Minister Bekir Bozdag, intelligence sources showed that Gulen, who has lived in Pennsylvania since 1999, was currently planning to escape to a country without an extradition treaty with Turkey.
He identified Australia, Canada, Egypt, Mexico and South Africa as countries where Turkey believes Gulen could seek refuge.