The bodies of the two men have now been identified
Prime Minister Gordon Brown has responded to criticisms that the UK did not do enough to try to free the two British hostages who died in Iraq.
He said the government had left "no stone unturned" in efforts to free five men held since May 2007.
It follows the release of the bodies of two British security guards, kidnapped along with the missing three men
There have been accusations that the UK's approach of not negotiating with hostage-takers endangers lives.
Mr Brown told GMTV that the government left "no stone unturned in its efforts to release the hostages and to work with the Iraqi authorities to use all possible means to free them".
He said during a press conference on Monday morning the hostage situation had been "at the top of the agenda" every time he spoke with Iraqi Prime Minister Nouri Maliki.
Former Liberal Democrat leader Sir Menzies Campbell said negotiations with those holding the remaining three hostages should now be stepped up.
So far, the government has said it is sticking to its line of not making "substantive concessions" to kidnappers.
A senior Foreign Office (FCO) official stated that Iraq, and not Britain, is the lead negotiator on the hostage crisis, the BBC's security correspondent Frank Gardner said.
Prime Minister Gordon Brown offers his condolences to the families
On Sunday the Foreign Office said the two bodies, handed over to UK officials in Iraq, were "highly likely" to be those of Jason Swindlehurst, from Skelmersdale, Lancashire, and Jason Creswell, of Portlethen, near Aberdeen.
Pathologists in Baghdad are still trying determine the cause and dates of death. The results may not be known until the end of the week.
The FCO said it had "grave concerns" about the safety of the remaining hostages - IT consultant, Peter Moore, and two bodyguards, who have been named only as Alan, from Dumbarton, and Alec, from South Wales.
The prime minister said: "There is no justification for hostage-taking and I call on those people who are holding the other Iraqi and British hostages to release them immediately."
The British government's policy of not making substantive concessions has been criticised by some and praised by others, including some North African countries who have attacked other European nations for paying huge ransoms to kidnappers.
But Sir Menzies said he would encourage the UK government to re-open contact with the hostage-takers.
He said "there is still the possibility that we can reach an accommodation which brings about the release of the other three. I would not, as it were, give up hope".
Freelance journalist James Brandon, who was held for 24 hours by militants in Basra in 2004, suggested Britain may need to alter its policy of never negotiating with hostage takers.
He said: "We've had British hostages kidnapped and killed in Iraq, in west Africa most recently. The present strategy isn't delivering results, it seems to be making life more dangerous for people, rather than safer."
Former Foreign Office Minister, Kim Howells, who was involved in trying to negotiate the hostages' release when they were first taken, said the government had done all it could to free them.
Frank Gardner, BBC security correspondent
"The Foreign Office approach is a softly-softly one. Questions will be asked whether this was the right approach.
"When the BBC's Alan Johnston was kidnapped in Gaza, we made a big song and dance about it. We put the whole story on the news the whole time.
"There were operational reasons why that wasn't advisable in this case.
"The kidnappers said they wanted a media blackout, which they kept breaking, but I think there will be a lot of soul-searching about this."
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