Police, however, indicated they are working to censor coverage of the demonstrations.
Prime minister Prayuth Chan-ocha’s government has already issued a decree that bans public gatherings of more than four people in Bangkok, outlaws news said to affect national security and gives authorities broad powers to detain people.
None of that has been able to keep the mostly young protesters from gathering across Bangkok over the past five days to push their demands, which also include constitutional changes and reform of the monarchy.
On Sunday, rallies spread to at least a dozen provinces outside Bangkok.
Mr Prayuth told reporters the state of emergency will remain only in Bangkok for now.
He said of the demonstrators: “I want to ask them for a few things: Don’t destroy the government and private properties and don’t touch the monarchy.”
Nevertheless, police said they were pushing forward with ways to flex their power, including seeking to invoke censorship measures to restrict reporting on the protests.
Deputy police spokesman Kissana Phataracharoen confirmed that police are forwarding a request to the appropriate agencies to take action against information providers that give what he called “distorted information” that can cause unrest and confusion in society.
Under existing laws, the National Broadcasting and Telecommunications Commission and the Ministry of Digital Economy and Society are empowered to ban broadcasts and block internet content.
Police themselves can also do so under the emergency decree, which went into effect October 15, a day after protesters heckled a royal motorcade in a once-unthinkable scene in a country where the monarchy is protected by strict laws and treated with reverence.
Mr Kissana spoke after a leaked copy of the censorship request, officially termed an order, circulated on social media.
The order, dated October 16 and signed by the chief of police, calls for blocking access to the online sites of Voice TV, The Reporters, The Standard, Prachatai, and Free Youth, and removing their existing content.
It also proposes a ban on Voice TV’s digital broadcasts.
All the outlets have been broadcasting live coverage of the protests.
Voice TV and Prachatai are openly sympathetic to the protest movement, and Free Youth is a student protest organisation. As of Monday, none have been blocked.
At least one local cable TV provider, however, has been censoring international news broadcasts during their segments on the Thai protests.
The Foreign Correspondents Club of Thailand said it was “deeply concerned” by the censorship threat, adding that it “makes the government appear heavy-handed and unresponsive to criticism, and could stir up even more public anger”.
Its statement added: “Bona fide journalists should be allowed to report important developments without the threat of bans, suspensions, censorship or prosecution hanging over them.”
In addition the emergency decree making protests illegal, authorities have also tried in vain to keep people from gathering by selectively shutting down stations on Bangkok’s mass transport lines.
It has also warned that it will take legal action against those who promote the protests on social media, including by taking photographs there or checking into them on social media apps.
Despite that, protest-related hashtags remain the most used on Twitter.
The protesters charge that Mr Prayuth, who as army commander led a 2014 coup that toppled an elected government, was returned to power unfairly in last year’s general election because laws had been changed to favour a pro-military party.
The protesters say a constitution written under military rule and passed in a referendum in which campaigning against it was illegal is undemocratic.
The protest movement became particularly controversial when it adopted the reform of the monarchy as a demand. The protesters want it to act within the checks and balances of democracy.
The monarchy has long been considered sacrosanct in Thailand, and is protected by a law that makes defaming senior royals punishable by a prison term of three to 15 years.
Mr Prayuth said the government is open to an extraordinary session of parliament to seek a solution to the current situation. It is not clear when that might be held.
