Hectic consultations were on in both parties a day after the assembly elections returned a split verdict that gave majority to none in the 70-member assembly.
While BJP emerged as single largest party winning 31 seats, its ally Akali Dal (Badal) bagged one constituency, leaving it four MLAs short of majority mark of 36.
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AAP on the other hand bagged 28 seats followed by Congress with eight. JD-U won one seat while the Mundka seat was won by an Independent.
After a meeting of top party leaders at Arvind Kejriwal's residence, AAP leader Yogendra Yadav said even if Lt Governor Najeeb Jung invites the party to form the government it will decline such an offer citing lack of majority.
"We are not going to form the government. We will sit in the opposition and play the role of a constructive opposition. As per the Constitution the largest party has to take the responsibility of forming government," Yadav said.
"We have not got majority so it is very surprising that the number one party (BJP) is not ready to form the government and telling us to do so," he said.
Kejriwal, who held another meeting with AAP's newly elected MLAs to discuss strategy, said they would prefer to sit in the opposition and face elections if the situation warranted.
Both BJP and AAP asserted that they would neither extend nor take support from each other.
Amid uncertainty in Government formation, senior BJP leaders also held series of meetings and maintained their earlier position that the party will not stake claim to form a government as it was short of a clear majority.
"We have no numbers. We do not want to purchase any MLAs," former BJP president Nitin Gadkari, who is party in-charge of Delhi, said.