Tony Blair has endorsed an Iraqi probe into leaked video footage showing Saddam Hussein's execution.
Saddam Hussein was hanged for crimes against humanity
The prime minister also gave his backing to Iraqi Prime Minister Nouri Maliki - who has said he wants to quit his position early.
But Downing Street refused to endorse Deputy Prime Minister John Prescott's claims that the manner of Saddam's execution was "deplorable."
Media watchdog Ofcom has launched a probe into coverage of the execution.
It said it had received 30 complaints from viewers.
No British broadcaster showed the actual moment that the deposed Iraqi leader was killed and not all of the broadcasters being investigated aired the taunting that took place before the execution.
BBC One's coverage received the most complaints, 11, with eight being made about BBC News 24.
News reports on Channel 4, ITV1, Sky News and US broadcaster Fox was also the subject of complaints.
Mr Prescott's description of the footage as "deplorable" has, meanwhile, been dismissed by Downing Street as his "personal" opinion.
But the deputy prime minister's words have increased pressure on the prime minister, who was holidaying in Miami, Florida when the execution took place.
Mr Blair, who earlier returned to Downing Street, has made no official statement despite criticism of his silence.
Conservative leader David Cameron said the way the execution was handled, with Saddam's opponents taunting him on the gallows, was "quite wrong".
He told BBC Radio 4's Today programme: "It was a matter for the sovereign Iraqi government how they dispense justice in their country.
"I am not in favour, personally, of the death penalty, and, like others, I found the pictures on the television frankly pretty grisly."
"And I think the way it was handled, clearly with people shouting and gesticulating was quite wrong and I am glad the Iraqi authorities are going to have an investigation and a review into this."
Mr Cameron said it was a matter for Tony Blair whether he commented on the execution or not.
He said Mr Blair "probably should" have commented but was "having a holiday" at the time.
"He has a deputy prime minister who has made clear his view and I am sure the prime minister will say something shortly," added Mr Cameron.
Labour MPs, including former ministers Glenda Jackson and Peter Kilfoyle, have also criticised the lack of a public reaction from Mr Blair to the events in Baghdad.
The row over the former Iraqi leader's hanging gained momentum amid reports from Baghdad that a guard present at the execution was being questioned over the footage.
The mobile phone images - in contrast to the official version of events - showed the former president being taunted by guards telling him to "go to hell".
They have sparked international condemnation, with the Vatican branding the leaked footage a "spectacle" violating human rights.
The US authorities in Baghdad have sought to distance themselves from the scenes at Saddam's execution.
Major General William Caldwell, the US military spokesman in Iraq, said: "Would we have done things differently? Yes, we would have. But that's not our decision. That's the government of Iraq's decision."
The White House said that Mr Bush has not seen the footage and the president refused to comment on it during a Washington press conference.
Meanwhile, Downing Street said Mr Blair backed the inquiry by the Iraqi government into what had "gone wrong" and that he fully supported Mr Maliki.
The spokeswoman added: "The Iraqi government is going to conduct an inquiry into the manner in which the execution was conducted.
"We fully support that decision and believe it is the right thing to do."
She added: "As they have said, there were obviously things that went wrong."
The spokeswoman also insisted that Foreign Secretary Margaret Beckett spoke on behalf of the whole government in saying the UK was against the death penalty but that Saddam had been "held to account".
Mr Blair's support for the Iraqi PM came after Mr Maliki said he would not seek a second term in a job he wished he could give up before even the end of the first.