The latest poll in the Times of India and the Economic Times forecast 169 out of 543 seats for the Congress Party, ahead of 165 for the Hindu nationalist Bharatiya Janata Party (BJP).
The socialist combination of the National Front and the Left Front is expected to win 145 seats in what now appears to be a cliff-hanger leading to a hung parliament.
"It's interesting to see opinion polls in the media finally supporting us," a senior Congress leader and industry minister, K Karunakaran, said.
Various opinion polls published before the elections showed the BJP emerging as the single largest party, although well short of a majority.
Voting took place in about 150 seats on 27 April, and 200 more on 2 May. The next phase is set for tomorrow. All but six results should be known by Saturday. Repeat polling was being held yesterday in 511 polling stations where the voting was marred by violence.
The Times poll combined a fresh round of surveying with findings of a previous opinion poll, which had predicted 142 seats for the Congress and 189 for the BJP. It came amidst a growing controversy surrounding Mr Rao's leadership of the party which has ruled India for all but four years since independence.
In a newspaper interview on Saturday, Mr Karunakaran said the Congress Party, recently hit by a spate of defections, would recover its old strength if Mr Rao quit its leadership. "We will have to find a new party president after the general elections," Mr Karunakaran said.
The party's electoral strategy triggered defections by senior party members, including a former commerce minister, P Chidambaram, a strong advocate of the economic reforms Mr Rao introduced in 1991.
Mr Chidambaram, who broke away over Mr Rao's alliance with Tamil Nadu state's ruling regional party, was quoted as saying that Congress "was in a state of limbo".
Analysts expect most former Congressmen to return to the party if Mr Rao resigns as leader.
"I believe most of them [the defectors] strongly believe in the ideology of the Congress Party," Mr Karunakaran said.