Pennsylvania-based Gulen and his Gulen movement has repeatedly been accused by the Turkish government of masterminding and steering a "parallel state" in Turkey - an alleged group of bureaucrats embedded in the country`s institutions, including the judiciary and the police, intent on undermining the government.
Davutoglu said that his meeting with Gulen happened during a weekend in September 2013 while he was in New York serving as Turkish Foreign Minister together with then-President Abdullah Gul for a United Nations General Assembly meeting.
"I met him to invite him to return to Turkey in order to take the necessary steps for all the tensions to cease and warned against the politicization of the elements in the bureaucracy [linked to the Gulen movement]," he said.
The premier said he told Gulen the only way to clear prejudices was to return to Turkey and be open to dialogue after doing so.
"I said that, once he returned, he and our Premier [Erdogan] could be in direct dialogue, but if not, his stay in the U.S. was making communication impossible and raising more concerns," he added.
Davutoglu said it was a principle for him that he never went to another city, street or meeting without the knowledge or permission of Gul -- "as Gul himself knows very well" -- while he was on an official visit.
"So, I had told him beforehand that I would go to Pennsylvania from New York and have such a meeting," he said.
He also said he had talked with then-PM Erdogan before he left for New York and told him that it could be useful to make such an attempt [to talk to Gulen] to "have the pieces fall in place and prevent any possible negativity".
"I also informed both about what we discussed following my return," he added.
Led by U.S.-based preacher Fetullah Gulen, the so-called Gulen movement has been under scrutiny in Turkey.
Officials linked to the movement are accused of conducting wiretaps of high-profile figures within the Turkish state as well as constructing a "parallel state" to overthrow the elected Turkish government.
An anti-graft probe targeted a number of high-profile figures in December 2013, including the sons of three former government ministers and leading Turkish businessmen.
The government has denounced the probe as a "dirty plot" constructed by the "parallel state".