Both Paswan and Minister of State for Rural Development Upendra Kushwaha said the new front stood no chance of making a mark in national politics.
Its leaders, they told the media, were "selfish" and had lost credibility among the people.
"It is nothing but an attempt by a group of selfish leaders to form a united front for survival," Paswan said.
Kushwaha said the new front showed its leaders had been rejected by the people. "They are all dejected and frustrated."
Both ministers said there was no match for Prime Minister Narendra Modi -- even if the proposed front of socialist parties became a reality. "No one can stop Modi's wave."
Paswan heads the Lok Janshakti Party and Kushwaha is president of the Rashtriya Lok Samta Party. Both are allies of the Bharatiya Janata Party.
Ahead of the winter session of parliament, leaders of the Samajwadi Party, Janata Dal-United, Rashtriya Janata Dal and Janata Dal-Secular have announced a united front to counter the Modi government.