CCAA112 is made up of several academic and activist groups. They comprise the Midnight University, Nitimon, Nitirat, People's Poets, Red Siam, Sang Sumneuk Writers, Santi Prachadham, Silpakorn Community for the People and Student Federation of Thailand.
Kritaya Archavanitkul, Mahidol University's Institute for Population and Social Research, said the amendment proposal has been drafted by a group of progressive legal scholars, the Nitirat (Enlightened Jurists).
"Taking into account studies [of other countries with royal families] from Japan to Europe, a different law to protect the dignity of the monarchy is needed," said Worachet Pakeerut, a key group member and a Thammasat University law associate professor.
He said the lese majeste law should be amended in line with international standards and democratic principles.
"Hopefully the campaign can help all sides speak their mind without fear of reprisals," he said, while pointing out the law has been used as political tool against rivals.
The lese majeste law, which falls under Article 112 of the Criminal Code, mandates jail sentences for defaming, insulting or threatening the King, Queen, Heir Apparent or Regent.
The bill proposed by the Nitirat group calls for a reduction in punishments for offenders.
Under the proposal, people found guilty of defaming the King will be subject to a jail term of no more than two years, or a fine of up to 50,000 baht, or both.
The jail term and the fine will be increased to no more than three years and 400,000 baht if the insults are advertised. People found guilty of spreading insults or hatred against the King will face a jail term of no more than one year, and/or a fine of up to 20,000 baht.
People found guilty of defaming the Queen, Heir Apparent or Regent will face a jail term of up to one year or/and a fine of up to 30,000 baht. The punishment will be increased to two years or/and a fine of up to 300,000 baht if the insults are advertised.
Those found guilty for spreading insults against the Queen, Heir Apparent or Regent will face a jail term of up to six months or/and a fine of up to 60,000 baht. The Nitirat group also proposed the Office of His Majesty the King's Principal Private Secretary be assigned as the sole agency which can file lese majeste cases.
A 51-year-old woman who joined yesterday's campaign with her family from Samut Songkram's Amphawa district said she and her family have signed in support of the amendment.
"The law has been widely politicised," she said. "Look at the people convicted under this law. Half are commoners speaking their minds, not well-educated or middle-class people."
Meanwhile, the cabinet wants state agencies to "improve" the way they conduct lese majeste cases.
State agencies should work together more closely, and treat such complaints as highly confidential, cabinet decided.
The number of lese majeste cases was rising, with many affecting the government politically, the meeting was told.