The UK is to urge the interim Iraqi government to abolish the death penalty which has just been reintroduced there.
Ms Clwyd says the decision to close al-Jazeera is "regrettable".
Ann Clwyd, UK special representative on human rights in Iraq, said she was "sorry" the penalty had returned.
"We will continue to lobby the government to abolish it as we do with other states," she told BBC Radio 4's Today Programme.
But she said she understood the interim government had a duty to bring the security situation under control.
She had recently met Iraq's deputy prime minister who, she said, told her there had been "a great deal of debate" and "soul searching" about the death penalty's re-introduction.
The interim government has brought back the death penalty, which was suspended after the fall of Saddam Hussein, for crimes including murder, kidnapping and drug dealing.
It is being seen as necessary to maintain law and order.
Ms Clwyd also said the decision to close down Arabic TV network al-Jazeera for a month was " regrettable".
She understood there were concerns about the way the network operated and claims that it breached basic "journalistic ethics", she said.
Saddam Hussein could face the death penalty
But action should be taken by independent regulation not government censorship, she told Today.
Ms Clwyd also said she was surprised that arrest warrants had been issued for two key Iraqi political figures, Salem Chalabi and his uncle Ahmed Chalabi.
Ahmed Chalabi is wanted on counterfeiting charges, and his nephew Salem Chalabi, the head of the tribunal trying Saddam Hussein, is sought on suspicion of murder.
Both men have denied the charges.
Salem Chalabi told Today the allegations against him were "ridiculous".
He denied ever meeting the man who he is alleged to have threatened to kill.
"I plan on returning, I just want assurances I will not be killed in a jail," Mr Chalabi added.
Ms Clwyd said both men would be ready to face the charges.
She warned they would be in danger if they were imprisoned in Iraq as so many former members of the regime are held in its jails.