Senator Kamnoon Sitthisamarn has asked the government to communicate directly with protesters regarding issues polarising the country while urging the prime minister to also address the matter.
During a meeting of the Senate on Monday, Mr Kamnoon said the placards held up by some of the protesters might cause distress to a lot of people in society and asked the prime minister how the government would deal with the issue.
The protesters' demands embodied the political conflicts that have existed in Thailand for the past 15 years, he said.
The Free Youth group and the Student Union of Thailand staged an anti-government protest on July 18, demanding the government dissolve the parliament, stop using oppressive laws and rewrite the constitution.
Deputy Defence Minister Gen Chaichan Changmongkol said the PM was concerned about the protest and warned that it must not involve the monarchy.
Meanwhile, Chairman of the Progressive Movement Thanathorn Juangroongruangkit denied the rumours that he was behind the demonstration and had paid the protest leaders.
Mr Thanathorn, however, said the Progressive Movement and the Move Forward Party supported the protest as they all wanted the constitution rewritten.
The politician urged people to help protect the pro-democracy protesters who might be prosecuted for violating the emergency decree and lèse majesté law.
Chief of the Metropolitan Police Bureau Pol Lt Gen Phukphong Phongpetra said investigators were deciding whether to summon the protest leaders for questioning.
Regarding an anti-government demonstration in front of the Royal Thai Army Headquarters on Monday, deputy police spokesperson Pol Col Kissana Phathanacharoen said he was concerned that there might be a third party behind the protest, though he did not elaborate.
The demonstration, also organised by the Free Youth group and the Student Union of Thailand, used loudspeakers and set up a small stage in front of the army headquarters on Ratchadamnoen Road.
The protest mainly attacked the military and its spending budget.
The protest leaders said they were not a "casual mob" as they were labelled by a former army spokesperson.