Mr Chavanond said the party had received information there was a plot to create chaos at the meeting with Mr Abhisit the target.
“An armed group also announced there might be a suicide mission to assassinate Mr Abhisit,“ he said.
“This shows Thai society is still rife with threats and violence, which have only increased over the years.
“We regret that we couldn't attend the meeting, but the safety of our leader is paramount,“ he said.
Mr Abhisit is no stranger to death threats, he said.
The former prime minister's life was threatened more than once in Pattaya and at the Interior Ministry when he was in office during the red-shirt riots, Mr Chavanond said.
Even after he stepped down, his life continued to be in danger as dissidents twisted facts to foster hatred.
It came to the point that a suicide mission was planned to eliminate him, even though the party is not the key that prevents an election from taking place.
A Facebook page called Lung Yim Ta Sawang states there will be an incident at the meeting, “for the sake of democracy”, he said.
When Mr Abhisit did not attend, the posts on that page were like those made by someone sitting in the meeting room.
“The meeting hasn't started because we have to wait for Abhisit. Shouldn't I ask Phi Sa-ngiam to shoot a couple of rounds so everyone runs home,“ the poster said, according to Mr Chavanond.
In the past, the Facebook page contained several posts hinting at violent acts which later turned out to be true.
These posts matched the party's own intelligence information.
Mr Chavanond said it is not right to push ahead with an election without solving the problems first.
“Pheu Thai has to answer how it expects the Democrat Party to contest the election when there are still safety concerns,“ he said.
On Wednesday, Mr Abhisit would send a message to all Thais asking them to start over and bring the country out of conflict, violence and risk of confrontations, he added.