A new book disputes Senate Majority Leader Harry Reid’s account of his attempts to persuade Barack Obama to run for president — saying they started a year earlier and played out differently than Reid has previously suggested.

“Game Change,” co-authored by journalists Mark Halperin and John Heilemann, reveals that Reid was pushing Obama in the summer of 2006 to consider running for president, suggesting that Reid was concerned early on that Hillary Clinton would lose the White House and undercutting the majority leader’s public stance that he was neutral in the race.

In his own memoir, “The Good Fight,” Reid writes that he talked to Obama in early 2007 about mounting a campaign. And unlike the reporters’ account, Reid portrays an exchange where Obama was wary about mounting a bid for president.

The revelation comes as the new book has disclosed deeply damaging comments Reid made to the reporters, where he said the country was ready for a black president — particularly one that was “light-skinned” with no “Negro dialect, unless he wanted to have one.” Reid immediately apologized for his remarks, and Obama and other Democrats have come to his defense. But the Nevada Democrat has come under ferocious criticism from Republicans, with RNC Chairman Michael Steele and Senate Minority Whip Jon Kyl (R-Ariz.) each saying on Sunday that he should step down as majority leader.

In both Reid’s book and in “Game Change,” Reid is shown as an early supporter of Obama’s presidential run — even though publicly, Reid insisted he was staying neutral in the race.

In Reid’s book, he writes that a 2007 conversation developed into whether Obama could be the next president.

“If you want to be president, you can be president now,” Reid says he told Obama. Reid says Obama replied, “I don’t know, Harry. I don’t think so.”

But in their new book, the reporters say that Obama was summoned to Reid’s office in July 2006 — and that Obama thought that he was about to get scolded by the majority leader.

As soon as Obama took his seat, the authors write, Reid told Obama: “You’re not going to go anyplace here. I know that you don’t like it, doing what you’re doing.

The authors write that Obama was not sure what Reid was talking about initially when he made clear that he didn’t think Obama was going to have a long career in the Senate. The two men spoke for 20 minutes, and Obama later was asked by his aide Robert Gibbs what they did wrong.

“Nothing,” Obama replied. “Harry wants me to run for president.”

“That whole meeting was about you running for president?” Gibbs said.

“Yeah,” Obama said, then grinned. “He really wants me to run for president.”

The discrepancies in the two books were first reported by Las Vegas Sun columnist Jon Ralston.

But Reid’s office downplayed the differences in the narratives.

“Sen. Reid had multiple conversations with Obama about running and doesn’t recall the exact date of when the first one occurred, but there’s no disputing the fact that he was one of the very first people to encourage Obama to run for president,” said Jim Manley, Reid’s spokesman.