Turkish government holds FETO responsible for the July 2016 defeated coup in Turkey.
Yildirim made the remarks following the fifth High-Level Strategic Cooperation Council meeting at Cankaya Palace in the capital Ankara on Thursday.
Pakistani Prime Minister Muhammad Nawaz Sharif co-chaired the meeting alongside Yildirim.
The Turkish premier highlighted the 70th anniversary of diplomatic relations between Turkey and Pakistan, saying both countries have always supported each other in "good and hard times”.
Yildirim also noted the expression of Pakistan’s support following the foiled coup. "All of Pakistani people, government and parliament of Pakistan stood by Turkey and Turkish people, displaying their historically-proven solidarity spirit," he said.
He said the terrorist group FETO remains a "huge threat" in around 170 countries that it functions.
"We know that brotherly country Pakistan is showing a meticulous approach to wiping out this terror group, which we think poses a national security threat and a threat to the public order in your country [as well]," he said.
FETO is widely believed to have orchestrated last year’s coup attempt against Turkey’s democratically-elected government, which left at least 248 martyrs in its wake and some 2,200 others injured.
Yildirim also offered condolences to Pakistanis over the spate of recent deadly terror attacks, describing them as the plague of our era.
Sharif thanked Turkey for its hospitality. He said Turkey was like his "second home".
"Our common bonds of faith, culture and history continue to deepen and nurture this relationship," Sharif said.
He reiterated that Pakistan remains in full solidarity with the country following the defeated coup.
Turkey's enemies are Pakistan's enemies, Sharif said, adding his country would continue its efforts against FETO.
He added Pakistan also supports Turkey’s fight against other terrorist groups like the PKK and Daesh.
As part of his three-day visit, Sharif will also hold a meeting with President Recep Tayyip Erdogan on regional and bilateral relations.
Yildirim said he and Sharif have given “necessary instructions” to their ministers for signing the free trade agreement (FTA) between the two countries within 2017.
He noted the sixth cooperation council will be held in Pakistan in 2018, while President Recep Tayyip Erdogan will also be in the country next month.
The High-Level Strategic Cooperation Council between the two sides was established during Erdogan's visit to Pakistan in 2009.
Following the latest meeting in Ankara, both sides signed agreements and memoranda of understanding in the fields of hydro carbons, environment, forestry, news agency cooperation, and exchange of financial intelligence and armed forces personnel.
The council meetings also resulted in six joint working groups in energy, finance, banking, transport and communications, culture and tourism and education fields.
A cooperation agreement between Anadolu Agency and Associated Press of Pakistan was also signed.