The expert, Dr.David Kelly, was a Ministry of Defence consultant on biological weapons and a former UN arms inspector in Iraq.
Glenda Jackson, a former minister under Blair, said the prime minister should "bite the bullet" and resign because the judicial inquiry into the circumstances into his death would paralyse the government.
Iain Duncan Smith, leader of the Conservative opposition, wrote to Blair demanding the recall of parliament from its summer recess to consider the fallout from Kelly's death. He also demanded a broader inquiry into the government's handling of intelligence on Iraq.
Kelly’s family said he had been under "intolerable pressure" after being grilled on Wednesday by a parliamentary committee examining the row over a BBC report that a February dossier on Iraq's alleged weapons of mass destruction had been "sexed up" by aides to Blair.
Kelly denied being the source for the story but admitted briefing Andrew Gilligan, the BBC defence correspondent whose report triggered the high-profile and still-unresolved row between the government and the national broadcaster.
The place where Kelly was
The pressure on Blair was increased by a statement from Kelly's family. "Events over recent weeks had made David's life intolerable and all of those involved should reflect long and hard on this fact," the family statement said.
It added, "It is hard to comprehend the enormity of this tragedy. We appeal now to everyone to afford us privacy to grieve in peace and come to terms with our loss."
British newspapers on Saturday accused Blair of using Kelly as a scapegoat and a diversion from this issue.
"Death of the dossier fall guy" was the page-one headline of the Daily Telegraph, while the Daily Mail attacked the government's treatment of Kelly under the headline "Proud of yourselves?".
The Financial Times termed the death "an immense blow" to the government and there was growing speculation that the affair would -- at the very least -- lead to the resignation of Alastair Campbell, Blair's director of communications and one of his closest aides.
Police said defence official Kelly, 59, whose body was found near his house on Friday, bled to death after apparently slashing his own wrist. A knife and a packet of painkillers often used in suicides were found near the body.