Velingkar, who heads Goa Suraksha Manch (GSM), a political outfit, was talking to a group of reporters in Panaji recently.
"The CM should take rest...It is shameful that he is retaining the chair," Velingkar added.
Both the seats fell vacant after Congress MLAs resigned to join the BJP in October last year.
"We will teach the BJP a lesson. The BJP-led government is untrustworthy, which has gone back on several of its promises," he alleged.
Velingkar, who was once a strong supporter of Parrikar, had fell out with him after the BJP-led state government decided to give grants to English medium schools.
Velingkar was leading a group of people who demanded that mother the tongue should be declared as the medium of instruction (MoI) in the elementary education in the state.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)