"We have sent four dossiers to the United States for the extradition of the terrorist chief. We will present them with more evidence than they want," Binali Yildirim told parliament.
Gulen has lived in self-imposed exile in the United States since 1999 and has denied any involvement in the putsch.
The Turkish premier called on the United States to "give up protecting that traitor" during a speech to his ruling Justice and Development Party (AKP).
"We know who staged and who ran it," he said, referring to the "parallel terrorist organisation" Turkey says is run by Gulen.
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Yildirim began his address by commemorating "democracy martyrs" and described parliament as a "veteran" after the building was extensively damaged by several airstrikes on the night of the coup.
"July 15 has shown the power of tanks were defeated by the power of people. This nation takes its strength from people, not from tanks.
"This parliament has seen plenty of coups but none of the coups have dropped bombs on parliament," he said, referring to the three attempts to seize power launched by the army since 1960 and the 1997 bloodless coup which forced an Islamist government out of office.
His speech was often interrupted by applause while party supporters waved Turkish flags in parliament.