Bill Clinton thought so little of President Obama — mocking him as an “amateur” — that he pressed his wife last summer to quit her job as secretary of state and challenge him in the primaries, a new book claims,

“The country needs you!” the former president told Hillary Clinton, urging her to run this year, according to accounts of the conversation included in Edward Klein’s new biography of Obama.

The title of Klein’s explosive, unauthorized bio of Obama, “The Amateur” (Regnery Publishing), was taken directly from Bill Clinton’s bombshell criticism of the president, the author said.

“Barack Obama,” Bill Clinton said, according to book excerpts, “is an amateur.”

The withering criticism is incredible, given the fact that Bill Clinton is actively campaigning for Obama’s re-election.

But according to the book, Bill Clinton unloaded on Obama and pressed Hillary to run against her boss during a gathering in the ex-president’s home office in Chappaqua last August that included longtime friends, Klein said.

“The economy’s a mess, it’s dead flat. America has lost its Triple-A rating . . . You know better than Obama does,” Bill said.

Bill Clinton insisted he had “no relationship” with Obama and had been consulted more frequently by his presidential successor, George W. Bush.

Obama, Bill Clinton said, “doesn’t know how to be president” and is “incompetent.”

But Hillary resisted the entreaties, according to two of the guests interviewed for the book.

“Why risk everything now?” a skeptical Hillary told her husband, emphasizing that she wanted to leave a legacy as secretary of state.

“Because,” Bill replied, his voice rising, “the country needs you!”

“The country needs us!” added Bill.

He later even joked about the prospect of having two Clinton presidential libraries — about the only time that Hillary cracked a smile.

“I want my term [at the State Department] to be an important one, and running away from it now would leave it as a footnote,” Hillary argued.

She said she had the option of running again in 2016.

But Bill wouldn’t let go.

“I know you’re young enough!” Bill said, his voice booming. “That’s not what I’m worried about. I’m worried that I’m not young enough.”

“I’m the highest-ranking member in Obama’s Cabinet. I eat breakfast with the guy every Thursday morning. What about loyalty, Bill? What about loyalty?” she responded.

“Loyalty is a joke,’’ Bill shot back. “Loyalty doesn’t exist in politics.”

Bill’s verbal battle with Hillary over the presidency, if anything, intensified when daughter Chelsea showed up with her husband, Marc Mezvinsky.

“You deserve to be president,” Chelsea said.

Bill was clearly pleased that Chelsea was on his side and vowed to have allies commission polls on a Hillary-Obama matchup.

“What are you trying to do — force my hand?” Hillary said.

“I want everyone to know how strong you poll,” Bill said.

Hillary said, “Go ahead and knock yourself out.”

The book’s explosive claims were shot down last night by spokesmen for the White House and the Clintons, who closed ranks last night.

Bill Clinton’s spokesman Matt McKenna said the excerpts were “totally and completely false” and called Klein “a known liar.”

Phillipe Reines, a spokesman for the secretary of state, noted that Hillary Clinton challenged the veracity of an earlier book Klein wrote about her, “Truth About Hillary.”

White House spokesman Eric Schultz accused Klein of making up facts to sell books.

“Nobody in their right mind would believe the nonsense in this one, especially since both Secretary Clinton and President Clinton have been loyal and supportive of the president at every turn.”

Klein, a former editor of The New York Times Magazine and Newsweek, defended the book and his earlier one as factually sound.

Meanwhile, today’s daily presidential Rasmussen Poll shows Mitt Romney ahead of the president with 50 percent to Obama’s 43 percent. It is the highest level of support the presumptive Republican nominee has received in his matchup with Obama as well as his largest lead.