The party also said that it was the responsibility of the BJP, which is the single largest party, to form the government.
"Even if Lt Governor Najeeb Jung invites the party to form the government it will decline such an offer citing lack of majority," said AAP leader Yogendra Yadav, after a meeting of top party leaders at Kejriwal's residence.
"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.
Yadav also strongly ruled out taking support of Congress to form government.
The BJP has also expressed its reluctance to stake claim, saying it did not have the numbers to provide a stable government.
BJP's Chief Ministerial candidate Harsh Vardhan had said last night that he will not stake claim to form a government as his party is short of a clear majority and would prefer to sit in the opposition than indulge in any "horse trading".
"...Since I don't have number I cannot stake my claim in forming my government in Delhi...Since I don't have the magic number of 36, I really cannot be a part of the government formation in Delhi," he had said.
The BJP emerged as the single largest party with 31 seats - four short of a majority as its ally SAD won one seat. AAP made a stunning debut by winning 28 seats in the Delhi Assembly polls and emerging as the second largest party ahead of the ruling Congress (8 seats), and barely behind the BJP.
The AAP's performance was capped by Kejriwal's thumping victory against Chief Minister Sheila Dikshit in her New Delhi constituency by a margin of 25,864 votes.
"We will play the role of a constructive opposition and will not seek or give support from any party to form the govt," Kejriwal told reporters in his first comments after results were declared.
(With PTI inputs)