Digital Economy and Society Minister Buddhipongse Punnakanta has become a target of criticism after his ministry blocked access to Pornhub, a well-known adult website based outside the country.
The ministry on Monday ordered all internet providers and mobile phone operators to ban all access to the website after the Criminal Court gave the ministry the green light to take action, because porn websites are illegal in Thailand.
As of Tuesday afternoon, more than 190 URL addresses of the website, which claims to be the world's leading free porn site, had been blocked under the DES order.
But instead of receiving praise, Mr Buddhipongse has been attacked for violating the right of the people to free access to the media.
"The Anonymous Party insists on the right to hold gatherings and the right to have access to all types of media," the group posted on its Facebook account on Tuesday. That freedom included media containing sexual content, as long as viewers were not forced to watch it, the group said.
It called for a rally at the Government Complex, at Chaeng Wattana, at 4pm in opposition to the ministry's action.
The Anonymous Party Facebook account is linked to rallies against the government. Its previous posts have included calls for all political activists to be released and a message urging all demonstrators to go to Bangkok Remand Prison to welcome those released from jail.
National artist Suchart Sawadsri, who is a government critic, on Monday posted a message on his Facebook account vaguely dragging the issue into politics. "How will Thai politics get better if Pornhub is banned?" he wrote.
Not everyone agreed.
Activist Nuttaa Mahattana on Tuesday argued on her Facebook page in support of the decision. Pornhub was an illegal website in Thailand and a source of online criminal activities, she said.
"Do not link this issue to politics and do not support the (website's) activities," she said.
"Democracy does not mean you can do anything at will with no responsibility," she wrote.
Mr Buddhipongse, who was in Phuket for a cabinet meeting, said on Tuesday he was doing his job and would not react to the critics. Many people had complained to the ministry about the website and some had even said the ministry was too slow to take action, he said.
Once Pornhub was blocked, tips on how to access it quickly began circulating on social media.