Parnoja is a member of the Moderates and a strong supporter of selling the state-owned power stations to American company NRG.
The initial vote on holding a no-confidence vote was signed by 45 MPs. The vote takes into account the NRG deal and Parnoja's role in it, stressing that he did not reveal public information about the consequences of the deal.
Commenting on the probable effect the vote could bring, Kulli Koit, government spokesman, said Parliament is to decide whether Parnoja is going to keep his position.
"Everything depends upon the majority of Parliament. It (must) approve the vote of no confidence to make Parnoja resign," Koit said.
The no-confidence centers on two documents - Parnoja's explanatory note and a record of witness interrogation.
Both relate to the case of Estonian scientist and dissident Juri Kukk, who died in a Soviet prison in 1981. Parnoja, who was one of Kukk's colleagues at Tartu University's department of inorganic chemistry, made several statements that might have led to Kukk's death, according to Kesknadal.
"Parnoja was a good specialist, and his opinion could determine Kukk's faith," said Heimar Lenk, editor-in-chief of Kesknadal.
According to Kesknadal, Parnoja told KGB in 1980 that Kukk, "as a person rejecting the ideology of the Komsomol could not deal with the teaching and bringing up of the young generation."
Seven years ago the Estonian daily Postimees also published the explanatory note. In 1993, Parnoja told the daily his testimony to the investigator was neutral, because he was not summoned to court on the basis of testimony as others were.
Lenk said the paper has several KGB documents concerning Parnoja, but only two of them are original.
"We published only the original documents. Now we are receiving calls and letters from the people related to Kukk's case, and they confirm Parnoja collaborated with KGB," said Lenk.
The documents were written by investigators, but signed by Parnoja. Parnoja himself has not denied answering KGB's questions. However, he said the statement he signed on March 25, 1980 in Tartu was presented in a different way.
Lenk said the documents could hardly influence the NRG deal, but they will definitely influence Parnoja's career.
"According to Estonian law, it is possible to sue a person on the basis of the documents published in the media," said Lenk.