(CNN) - Gene Sperling, a senior economic aide to the president, said he hopes he and veteran journalist Bob Woodward can look past their recent dustup, which made national headlines and divided the inside-the-Beltway crowd over the interpretation of one word: "regret."
"Bob and I have known each other for 20 years, and we've always had a friendly and respectful relationship," Sperling said Sunday on CNN's "State of the Union."
"Anyone who looks at the e-mails that went from me and came back from him can see that there's respect and friendliness," he continued.
In an appearance on CNN's "The Situation Room" on Wednesday, Woodward said that his recent reporting on the forced spending cuts known as the sequester had irked the White House and led to what he described as a hostile e-mail exchange between him and Sperling (although he would not name Sperling at the time).
"They're not happy at all," Woodward said.
"It was said very clearly, 'You will regret doing this,' " he continued, implying a threat.
In the week before the deadline for the sequester to kick in, Republicans and Democrats engaged in a public blame game, with each side faulting the other for the initial idea of the spending cuts back in August 2011.
Woodward, who literally wrote the book on the 2011 budget battle, published an op-ed in which he authoritatively stated that White House was the originator of the idea and went on to say that President Barack Obama was reneging on his pledge not to push for new revenues in any sort of deal to avoid the cuts.
Politico published the e-mails on Thursday, which a Democrat with knowledge of them identified as between Woodward and Sperling. White House press secretary Jay Carney did not dispute that the published e-mails were accurate.
The part of the e-mail from Sperling to Woodward that used the word "regret" said: "But I do truly believe you should rethink your comment about saying … that (Obama) asking for revenues is moving the goal post. I know you may not believe this, but as a friend, I think you will regret staking out that claim."
A White House official said Wednesday evening - after the CNN interview - that the e-mail Woodward referred to "was sent to apologize for voices being raised in their previous conversation.
The note suggested that Mr. Woodward would regret the observation he made regarding the sequester because that observation was inaccurate, nothing more. And Mr. Woodward responded to this aide's e-mail in a friendly manner."
As to why Woodward didn't interpret the e-mail in the spirit that Sperling said it was written, Sperling said, "I can't explain that entirely, but I'll say the following: I think he's a legend. I hope that him and I can put this behind us, and I hope that it helps all of us focus on the issues that Bob and I care more about, which is how we come to the type of budget agreement that will help our economy, help jobs, help middle-class Americans."
Sperling told CNN's chief political correspondent Candy Crowley that he had not spoken to Woodward since their e-mail exchange went public.
"I hope to," he said.
During the same hour Sunday, Woodward appeared on a separate program in which he offered an invitation to Sperling.
"He's a peacemaker," Woodward said Sunday on CBS's "Face The Nation." "I am in the business of listening, and I'm going to invite him over to my house if he'll come and hopefully he'll bring others from the White House, maybe the president himself, and we can - you know, talking really works."
- CNN’s Gregory Wallace contributed to this report.
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