Gautam is a former BJP legislator who has posed a challenge to the less than two-month-old BJP-JJP alliance government in Haryana.
"Whatever I have to say, I had conveyed. Now there is no question of rethinking on my decision," he told the media.
Gautam stepped down as Vice-President of the Dushyant-led JJP. But he clarified that he had only resigned as the party's national vice president, but not given up the party membership.
On being asked about reconciliation, he added: "There is no question of meeting the party leadership. I have resigned from the post that holds no relevance (in the party)."
Upset with functioning of the government, he said on Wednesday the alliance was "sealed in a mall secretly", indirectly hinting that except Dushyant, no legislator was aware about the development.
Reacting to the development, Dushyant said he has not received any resignation.
"I have also seen that video. Gautam is the senior-most leader of the JJP. If he has any grievance, he can raise within the party. His resignation has not been received at the party office," Dushyant told the media here.
"If we get his resignation, senior leaders of the party will meet him and discuss the issue with him. He is our senior and we don't feel bad about his saying," he said, adding "he (Gautam) played an important role in strengthening the party...will sit and discuss".
Gautam, 73, defeated BJP's sitting Finance Minister Captain Abhimanyu from the Narnaud constituency in Hisar district with a margin of 12,029 votes.
His sudden outburst against Jannayak Janta Party (JJP) leader Chautala, 31, is over 'deliberate' sidelining of party's legislators and taking over all plum posts.
Without mincing words, Gautam categorically said Dushyant should not forget that he became Deputy Chief Minister with the support of the nine legislators. At the same time, he clarified that he was not against the formation of the BJP-JJP government.
Sources said Gautam was the front-runner for a Cabinet berth in Manohar Lal Khattar's first Cabinet expansion in November in which 10 ministers, including one from the JJP, a lone woman and an independent, were inducted.
"Gautam was deliberately sidelined in the new government formation owing to influence of Captain Abhimanyu, who does not want anyone from his constituency to get into the government on any crucial position," a senior BJP leader told .
He said Gautam's induction into the Cabinet was dropped at the last minute owing to reluctance of Khattar.
"I am stepping down as national vice-president with immediate effect. But I will remain in the party. The situation has not come to that point that I quit the party and resign as MLA," he said.
Slamming Dushyant for keeping 10 portfolios with him, he said: "He should realise there are nine other MLAs in the party. These MLAs too were chosen by the people. Most party MLAs are disappointed over the issue."
He also said Dushyant was toeing the line of his ancestors who cannot see someone else growing politically other than himself.
Sources in the JJP said Gautam played a crucial role in Dushyant's victory and of other party legislators.
The saffron party's post-poll alliance partner JJP, a splinter faction of the state's once prominent regional outfit Indian National Lok Dal (INLD), got a lone minister in Anoop Dhanak, who has been allocated the less important Archaeology and Museums portfolios.
Both Khattar and Dushyant took oath of office on October 27.
Dushyant is the great grandson of former Deputy Prime Minister and the tallest Jat leader, late Devi Lal, whose INLD has been politically marginalised in the recent concluded Assembly elections in Haryana.
But INLD's offshoot and a year-old JJP, led by Dushyant Chautala, sprang a surprise by winning 10 seats in the 90-member Haryana Assembly.
In a post-electoral alliance, the JJP has extended support to the BJP, which won 40 seats, six short of the majority mark.
The Cabinet can have 14 members, including the Chief Minister and the Deputy Chief Minister, with two slots kept for future expansion.
Political observers say Gautam's outburst at this point may be to secure a Cabinet berth.
( With inputs from IANS )