The group, which includes lawmakers from six parties, is expected to put down motion on Monday in the House of Commons calling for a parliamentary committee investigation. The motion will then be debated on Wednesday in the lower house of parliament in a time slot allotted to the Scottish National Party (SNP).
According to SNP Member of Parliament Alex Salmond, "an example should be set, not just of improving government but holding people to account."
The motion could lead to Blair being stripped of his membership of the Privy Council.
The United Kingdom was part of a US-led coalition, which also included Australia and Poland, that invaded Iraq in 2003, without a UN mandate, after accusing then-Iraqi leader Saddam Hussein of possessing weapons of mass destruction, which were never found.
The Chilcot inquiry released in July 2016 after six years of deliberation, found that the UK government under Blair's leadership made a mistake by invading Iraq in 2003, as the decision to join the war was taken on the basis of flawed intelligence data and assessments.