Neither Twitter nor Facebook currently have an office in the country, although Facebook has staff in London who deal specifically with Turkey.
Both are popular in the country and were widely used by citizens seeking information about the protests at a time when mainstream Turkish media provided little or no coverage of the events.
On Wednesday Mr Yildrim said: "Facebook has been working in coordination with the Turkish authorities for a long time... We don't have any problem with them."
It led to speculation that the social network had provided the authorities with data on protesters, something the firm was quick to deny.
It said that it had not been asked by the Turkish government to provide any users' data following the protests.
It has closed down some pages related to activism in Turkey, but only, it said, because they had had "fake profiles".
"More generally, we reject all government data requests from Turkish authorities and push them to formal legal channels unless it appears that there is an immediate threat to life or a child," it said in a statement.
Social networks and other technology firms are attempting to rebuild trust with users following allegations that large amounts of data was handed to the US National Security Agency under a surveillance program known as Prism.