The centre-left candidate Prodi said on Friday he was glad "the game is over".
He added that "it's time to recognise our victory so that this strange comedy can end and we can move on like we should."
But a defiant Silvio Berlusconi told a crowd of supporters shouting "Silvio! Silvio!" outside his Rome residence: "We are carrying on. We will resist."
He refused to concede after the centre-left opposition won a razor-thin majority in the April 9 - 10 election, demanding a check of "disputed" ballots - papers on which the voting intention was deemed unclear by scrutineers.
But after four days of political stalemate, the Interior Ministry said the number of ballots in question for the lower house of parliament was 2,131, not enough to overturn Prodi's 24,000-vote majority.
The ministry said in a statement it had made a mistake when it initially estimated there were 43,028 disputed ballots.
In a letter to Italian daily Corriere della Sera, Berlusconi criticised Prodi for declaring victory and reiterated calls for a coalition between the right and left, something Prodi has rejected, saying he has a mandate to govern on his own.
"We are at a standstill, a situation in which, at least based on the number of votes, there are neither winners nor losers," Berlusconi said in the letter, to be published in the newspaper's Saturday edition.
Prodi said his bloc was ready to talk to the centre-right but that Berlusconi would have to concede defeat first.
Berlusconi repeated calls for a
coalition between right and left
Centre-left officials said the next step would be an official confirmation of the election results by the Court of Cassation, Italy's highest court for legal appeals.
That is not expected to come before next week at the earliest, a court official said on Friday.
Berlusconi's office declined comment on the Interior Ministry statement but pointed out that all election data was still preliminary ahead of the official court confirmation.
Berlusconi said earlier this week the result must change due to what he called widespread fraud, but most of his allies have shown no taste for a recount.
Nonetheless, some hardcore supporters maintained hope that the tenacious media tycoon could somehow prevail.
Mirko Tremaglia, the minister for Italians abroad, said Italy should rerun the election among overseas voters - whose support enabled Prodi to snatch a narrow victory in the upper house - because 10% had not received ballot papers.
Prodi, who has been seen smiling and relaxed in his northern hometown of Bologna, has already received congratulatory calls from foreign leaders, including those of France and Germany.
In his letter to Corriere, Berlusconi said a coalition between his bloc and Prodi's could just be temporary.
"A partial accord, for a limited time, to address the country's pending institutional, economic and international deadlines, should not be ruled out on principle."
Although it won by a handful of votes, a recent change to the electoral law introduced by Berlusconi means Prodi will have almost 70 more seats than the centre right in the 630-seat lower chamber.
In the Senate, Prodi has just a two-seat majority.