Lord Hutton said he would ask Blair to give evidence about a government decision naming Kelly as the possible source for a disputed BBC news report on the government's handling of intelligence on Iraqi weapons.
The ministry's decision placed him under intense media scrutiny and led him to give testimony before a parliamentary committee.
Blair's office said the prime minister "will cooperate fully with the inquiry."
Hutton made clear that he planned a wide-ranging inquiry not just into Kelly's death, but into the government dossier on Iraqi weapons which was at the core of the dispute that brought Kelly into the spotlight.
Hutton said he would also seek to question Defense Secretary Geoff Hoon and Blair's communications director Alastair Campbell.
"At some stage in the course of the inquiry, I propose to ask the prime minister and the Secretary of State for Defense Mr. Geoff Hoon to give evidence of their knowledge of the discussions that took place and the decisions which were taken in relation to Dr. Kelly," he said.
Blair said earlier this week that he did not authorize the identification of Kelly as the source for the BBC report.
"I did not authorize the leaking of the name of David Kelly," Blair told reporters on a flight from Shanghai to Hong Kong.
The microbiologist's body was found July 18 with his left wrist slashed. Two days later, the BBC confirmed that Kelly was the unidentified source for its report.
Hutton said he would explore how BBC journalist Andrew Gilligan compiled his report based on the Kelly interview.
Hutton said journalists could follow the proceedings of the inquiry,
which will get under way after Kelly's funeral, scheduled for Wednesday.
He added that the proceedings would be made available on a Web site.
"I should emphasize that this is an inquiry to be conducted by me," Hutton said. "It is not a trial conducted between interested parties who have conflicting cases to advance. I do not sit to decide between conflicting cases, I sit to investigate the circumstances surrounding Dr. Kelly's death."
Before the start of Friday's hearing at the Royal Courts of Justice, Hutton asked for a minute of silence to honor Kelly.