The junta-appointed NRSA advisory council plans to meet executives from the two companies in the next three months, council member Major General Pisit Paoin told Reuters.
The government has been granted court orders for the removal of content that damages the country and the monarchy and affects peace and order, which companies have rarely complied with. The firms would be asked to in future respond quickly to such rulings, he said.
Thailand’s junta has faced repeated criticism for what rights groups say is a deepening slide into authoritarianism since the army took power in May 2014.
Its previous attempts to get social media platforms to take down political postings have been largely ineffective, although the country has blocked thousands of websites hosting lese majeste content.
Numbers of people arrested under the laws against criticizing the monarchy have also risen sharply.
Thai representatives for Facebook and Google could not immediately be reached for comment.
Thai authorities made a similar request over content on Jan. 22 to technology giant Google, which owns the YouTube video sharing platform, Pisit said.
Authorities have also increasingly cracked down on criticism of the junta.
A former politician from the Pheu Thai party of deposed Prime Minister Yingluck Shinawatra was charged on Friday for violating the country’s Computer Crime Act for sharing on line a video mocking junta leader General Prayuth Chan-ocha.