Tony Blair was forced to make the pledge on Wednesday during parliamentary questions by opposition leader Michael Howard.
The Conservative leader pinned Blair down over suspicions that he authorised the leaking of Kelly's name as the source of a BBC report that alleged the government exaggerated the Iraqi weapons threat.
The weapons expert killed himself shortly after being outed, hurling Blair into the worst political crisis of his more than six years in office.
"The prime minister has said that a minister in a government he leads should resign if that minister lied to parliament," said Howard. "Does that apply to the prime minister himself?"
To which Blair replied: "Of course it applies to me, as it applies to all ministers."
"Of course it (Blair's pledge to resign if proven a liar) applies to me, as it applies to all ministers"
British prime minister
Howard's grilling centred on a statement that Blair made to reporters during a tour of East Asia four days after Kelly's body was found.
"I did not authorise the leaking of the name of David Kelly," said Blair on a flight from Shanghai to Hong Kong.
But the most senior civil servant at the Ministry of Defence seemed to contradict Blair's statement when testifying before the inquiry into Kelly's death.
Sir Kevin Tebbit said Blair had chaired a meeting where the decision was taken to expose Kelly to the press, as the BBC's source.
And in giving evidence to the Hutton Inquiry, Blair himself said he took full responsibility for the naming of Kelly to two parliamentary committees that were looking into the radio report.
The prime minister was also grilled over a late submission by his government to the inquiry which is due to report shortly.
Blair's official spokesman admitted Downing Street had sent information to senior judge Lord Hutton after he had concluded his investigation last Autumn. But he denied it included any new evidence.
Howard believes Blair could be
criticised in the Hutton report
However, opposition Conservatives demanded its publication and accused Blair of trying to pre-empt Hutton's findings.
Speculation is rife that the prime minister's team wanted to put their slant on the evidence given by Sir Kevin Tebbit.
Meanwhile, an inquiry official said Lord Hutton would make a statement later on Wednesday on the government's intervention.
British political life is all but frozen in anticipation of the report.
It is due to be released this month and could point the finger of blame at senior government figures.
No publication date has been named, serving only to increase the tension.