The Senate speaker sought police protection for senators and their families who said they were threatened after the prime ministerial vote last Thursday, and senators are filing complaints against those they believe responsible.
Senate Speaker Pornpetch Wichitcholchai said on Monday that senators told him that they and members of their families were threatened by individuals, their privacy was infringed upon and people were watchig their residences and business premises.
He decided to seek police protection for them, and police were cooperative, he said.
"I hope that those who threaten and interfere with other people will stop it, and there will not be any more criminal offences or disputes," Mr Pornpetch said.
Reports of threats being made against senators emerged after only 13 senators voted in favour of sole prime ministerial candidate Pita Limjaroenrat, leader of the election-winning Move Forward Party, in the joint sitting of the Senate and the House on July 13.
Mr Pita's eight coalition allies had 312 votes in the House. With support from only 13 senators he fell short of the needed majority of the two chambers by 51 votes. Most senators abstained from the vote.
Mr Pornpetch said on Monday that 33 senators were officially absent from the July 13 joint sitting.
He said two went were at a meeting in Beijing that he aproved, six were senior officials of the armed forces who had other important duties that day, nine took leave for private business overseas and had not been informed of the joint sitting beforehand, and 16 senators took sick leave.
On July 13, 43 senators did not cast a vote, showing that 10 of them were present at the meeting but chose not to vote, Mr Pornpetch said.
A group of senators told reporters thy were gathering evidence to support legal complaints against the people who posted threats against them and their families after Thursday's vote.
Among them, Senator Seri Suwannapanon said senators would not tolerate the bad behaviour that was ruining the nation, society and the beautiful lifestyle of Thai people.
The vote for prime minister was a parliamentary process. After the vote, there was undesireable behaviour, including threats to senators and representatives. "This impacts on the personal rights of semators and their families," Mr Seri said.
On Monday morning he filed defamation lawsuits against two lawyers he said had heavily criticised him. He sued each of them for 500,000 baht.
"There will be criminal and civil lawsuits against everyone who made accusations on social media, to send the message that freedom of expression must neither affect nor damage others," Mr Seri said.
He said there were threats against senators' businesses, although most vendors and workers at those places had voted for the Move Forward Party.
Senator Somchai Sawaengkan also said senators were gathering evidence to support complaints. The daughters of some senators even received rape threats, which was malicious, he said.
"Everyone who did this will face the consequences. Do not apologise. The price to be paid is high for posing threats and danger to others," Mr Somchai said.
"It is time to change society. Freedom of criticism does not mean freedom to threaten people who have different opinions," he said.