Libby, the vice-president's former chief of staff, was later convicted of obstructing the investigation into the leak and received a two-and-a-half year prison sentence, although that was commuted by George Bush, the US president.
Valerie Plame, the CIA operative, says the White House leaked her identity as retribution for criticism from her husband, Joseph Wilson, a former US diplomat, of Bush's reasons for going to war in Iraq.
John Conyers, a Democrat and the committee's chairman, asked McClellan to testify about details that appear in his book: What Happened: Inside the Bush White House and Washington's Culture of Deception.
|Valerie Plame's identity was leaked to the media [EPA]
The book includes McClellan's claim that he was instructed to mislead the public about the roles of Libby and Karl Rove, a former presidential adviser, in the leak of Plame's identity and its aftermath.
Mclellan said Andy Card, the former White House chief of staff, told him the president and vice-president wanted him to publicly say that Libby was not involved in the leak.
"This White House promised or assured the American people that at some point when this was behind us they would talk publicly about it," McClellan said of the leak.
"And they have refused to.
"And that's why I think more than any other reason we are here today and the suspicion still remains."
McClellan said he didn't know if a crime was committed and does not believe that Bush knew about or directed the leak.
When asked about Cheney, he replied: "I do not know. There's a lot of suspicion there.''
White House dismissal
The White House was dismissive of the committee's hearings and McClellan himself.
"I think Scott has probably told everyone everything he doesn't know, so
I don't know if anyone should expect him to say anything new today,'' Tony Fratto, a spokesman said.
Libby was convicted of perjury, obstruction and lying to the FBI in its investigation of the leak
Last July, Bush commuted Libby's sentence, sparing him from serving any time in prison.
"It was special treatment," McClellan said of the commutation.
"This undermines our system of justice, " he added.
McClellan was Bush's press spokesman from 2003 to 2006 but he has since been critical of the president's decisions, particularly over the war on Iraq.