The Turkish government has asked Twitter to set up an office inside the country so company representatives can be reached more easily.
Both Twitter and Facebook were used to spread information during recent anti-government protests.
Several dozen tweeters were arrested following the protests, according to local media reports.
Turkish Prime Minister Recep Tayyip Erdogan has previously described Twitter as a "scourge".
On Thursday, Transport and Communications Minister Binali Yildrim said: "When information is requested, we want to see someone in Turkey who can provide this.
"There needs to be an interlocutor we can put our grievance to and who can correct an error if there is one."
Twitter declined to respond to the government request on Wednesday, but a person familiar with the company said it had no current plans to open an office in that country.
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.
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