Conte, who led Juventus to the Serie A title last season, is accused of failing to report match-fixing in two games in the 2010/11 season when he was coach of Siena, then in Serie B.
On Wednesday, the Italian football federation (FIGC) tribunal said a proposed three-month ban agreed between Conte's lawyers and the federation prosecutor Stefano Palazzi was insufficient.
It called for them to come up with a tougher penalty proposal or to go to a full sporting trial.
Frantic negotiations failed on Thursday and Juventus President Andrea Agnelli blasted the federation, accusing it of incompetence and launching an unjustified "new attack" on the club.
"It appears that the FIGC and its system of sporting justice continue to operate in complete disregard of law and equality," said Agnelli in a statement.
He said the rejection of Conte's plea bargain "is testimony to the complete inadequacy of the sporting justice system and the federation within which it operates."
"Once again, I detect an inability to interpret the requirements of today's top-level professional game."
"Having chosen to make a plea bargain in order to limit the damage of an antiquated and contradictory system of sporting justice, one is confronted with a dictatorial system that deprives the club and its employees of any right to defend themselves and their honour."
The FIGC then issued a reply defending itself.
"The FIGC and its organisations operate with integrity and within full compliance of the statutory rules which guarantee the independence and autonomy of the sporting justice," it said.
"The judgements of the president of Juventus Andrea Agnelli are not acceptable and go beyond the legitimate exercise of free speech."
The federation has said it aims to reach a verdict in the Conte case by August 10.
Juventus were stripped of the Serie A titles they won in the 2004/05 and 2005/06 seasons following the so-called Calciopoli match-fixing scandal.
The matches involved in the charges were between Novara and Siena in May 2011, which ended 2-2, and between Albinoleffe and Siena in the same month which ended in a 1-0 defeat for Siena.
On Wednesday, Siena had six points deducted for the forthcoming Serie A season after their plea bargain was accepted at the second attempt.
In total, 13 clubs and 45 players and training staff are facing disciplinary charges over the latest match-fixing allegations.
The "Calcioscommesse" scandal echoes earlier match-fixing cases which tarnished Italian football in the 1980s and before the 2006 World Cup.
Prosecutors believe an international gambling ring paid players to throw matches. Dozens of current and former players in teams ranging from the Serie A top division down to the lower leagues may have been involved, according to investigators.
