The development came after three Congress legislators reportedly expressed their desire to extend outside support to the Arvind Kejriwal-led Aam Aadmi Party.
The AAP has 27 legislators whereas the Congress has eight in the house of 70.
"We will not support the AAP at any cost. When we gave them the opportunity, they ran away," Delhi Congress chief Arvinder Singh Lovely said.
"There is consensus in the party over this issue. It is up to the Bharatiya Janata Party to form the government," Lovely told reporters.
Meanwhile, Congress general secretary Ajay Maken tweeted: "Under no circumstances, Congress will support the AAP to form the government in Delhi."
Earlier, a section of AAP legislators - not in favour of re-elections - wanted the party to form the government with help of the Congress. The AAP officially declined to seek support.
Delhi has been under President's rule since February when Chief Minister Arvind Kejriwal resigned over his failure to pass the Jan Lokpal bill in the assembly.