The protest was a "symbolic act", and not an attack, said Information and Communication Technology Minister Uttama Savanayana.
"It may come from certain groups with their view or concerns related to the single gateway," he told reporters, stressing that the single gateway was still just an idea.
"At the moment the feasibility studies have yet to reach any conclusion."
Websites forced offline included those of the government, the armed forces, the defense ministry and the military's internal security agency.
The single gateway proposal has triggered concern that social media and business communications could be monitored. The protest urged internet users to go to the government websites and overload them by refreshing the page repeatedly.
"We invite fellow gamers to show we don't want a single gateway, so that the Thai government will listen to our problems," one Facebook group posted in an appeal that has drawn more than 120,000 "likes".
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Draconian Thai cyber legislation has existed since 2007 and is often used to police websites and stamp out criticism of the country's revered monarchy, which is protected by strict lese-majeste laws being strongly enforced by the junta.
Thousands of websites have been blocked in recent years, coinciding with a decade-long political conflict in which social media and the Internet play a crucial role. Thailand has 35 million internet users among its 67 million people.
Experts say the single gateway would let authorities screen and filter content more easily, but risked slowing internet speed and disrupting business.
Uttama said there would be no interference with social media and business communications, adding that Prime Minister Prayuth Chan-ocha, who led the coup, was concerned about inappropriate internet use.
Prayuth had asked government agencies to "find measures to take appropriate care and raise the youth of the nation to learn, use and access technology in the most beneficial way," he said.