Gordon Brown has condemned as "deplorable" the way in which Saddam Hussein's execution was conducted.
Gordon Brown and John Prescott have both condemned the hanging
The chancellor told BBC One's Sunday AM the manner of the former Iraqi leader's hanging was "completely unacceptable".
Mr Brown, whose comments come after mobile phone footage of the hanging showed Saddam Hussein being taunted, said he was against the death penalty.
Deputy PM John Prescott has already condemned the scenes as deplorable, but Tony Blair has yet to comment.
Mr Brown said: "Now that we know the full picture of what happened, we can sum this up as a deplorable set of events.
"It is something, of course, which the Iraqi government has now expressed its anxiety and shame at.
"It has done nothing to lessen tensions between the Shia and Sunni communities."
He added: "Even those people unlike me who are in favour of capital punishment found this completely unacceptable and I am pleased that there is now an inquiry into this and I hope lessons in this area will be learnt, as we learn other lessons about Iraq."
On Wednesday the Iraqi government began an inquiry into the unofficial footage, which appeared on the internet hours after the execution.
Iraqi PM Nouri Maliki has also said his government could review relations with any country which criticised the execution of ex-leader Saddam Hussein.
He said the hanging was a "domestic affair" for the benefit of Iraq's unity.
Last week Mr Prescott, in charge of the country while the prime minister was on holiday, also described the filming of the execution as "deplorable".
Mr Blair has said he will speak about the 30 December execution next week, although Downing Street said the PM supported an Iraqi investigation into the hanging.
A spokeswoman said that Mr Blair will say something about the execution at "a time of his choosing".
BBC political correspondent Laura Kuenssberg said Mr Brown's comment "not only pre-empts Tony Blair but also sort of boxes him into a corner".
The prime minister's silence has already prompted the Liberal Democrats to question his leadership, she said.
Education Secretary and deputy leadership candidate Alan Johnson told the Observer he also had concerns about the way the execution was carried out.
"I agree with John Prescott's remarks about the way it was handled and I am an opponent of the death penalty.
"But it was a matter for the Iraqi people to make that judgment.
"What happened at the end shouldn't detract from the terrible crimes that Saddam committed."
Initial Iraqi government film showed Saddam being executed in a relatively dignified manner, however mobile phone footage emerged showing Saddam - a Sunni - being taunted with Shia slogans.
Following Mr Brown's remarks, Liberal Democrat leader Sir Menzies Campbell said: "The prime minister's continuing silence is deafening.
"His unwillingness to condemn the shameful scenes surrounding Saddam Hussein's execution does him no credit."