Mr Straw repeated his appeal for the 74-year-old peace campaigner's release and renewed a call for his captors to get in touch.
He said: "We have people in Iraq itself and in the region and they are ready to hear from the kidnappers."
The call came as the group holding Mr Kember and three other men were reported to have extended the deadline for his execution by two days, to Saturday.
It was a hopeful sign for UK officials as the message appeared to be a direct response to Mr Straw's previous statements.
They are thought to be taking the extension of the deadline at "face value" and pressing on with their strategy of encouraging the kidnappers to make contact.
Today Mr Straw said it was "hard to imagine the terrible distress" being suffered by Mr Kember's wife Pat, adding: "Our thoughts and prayers are with them.
"As I have said before, if the kidnappers want to get in touch with us we want to hear what they have to say."
Mr Kember, from Pinner, north-west London, was seized in Baghdad on November 26with James Loney, 41, and Harmeet Singh Sooden, 32, both Canadians, and anAmerican, Tom Fox, 54.
He had travelled to Iraq as a gesture of solidarity with the Christian Peacemaker Team (CPT), a Canadian-based international peace group.
The Swords of Righteousness Brigade, which is holding them, had threatened to kill the men if Iraqi prisoners were not freed from US and Iraqi jails by today.
Yesterday a poor quality video broadcast on Arabic TV channel Al-Jazeera showed four people dressed in orange boiler suits, although their faces could not be seen, accompanied by a message saying that the deadline had been extended.
The apparently confused and rambling message said: "We have heard the statement of the British foreign minister and to prove to the world that he was not serious in what he said... and to forego any attempt by any liar to cheat the world we are hereby extending the deadline for two more days to distinguish between one who tells the truth and the liar."
The message is being seen as hopeful because it gives the kidnappers more time to contact British officials.
Mr Straw yesterday said that the meaning of the latest statement was " not clear".
But it does seem apparent that the kidnappers have singled out what he has said in public and that they are now at least willing to trade statements.
Officials will now be hoping that the next stage will be encouraging them to get in touch on the ground.
The Muslim Association of Britain, which has dispatched leading member AnasAltikriti to the Middle East to try to secure the release of the hostages,welcomed the extension of the deadline.
Mr Altikriti, who has already won the backing of Iraq's leading Sunni Muslim organisations and appeared on Arabic TV, travelled to Amman, Jordan last night as part of his efforts.
In a statement today, the MAB said: "The Muslim Association of Britain welcomes the announcement by the group holding the four western hostages including Briton Norman Kember, in Iraq, of a 48-hour extension to the previously set deadline.
"The envoy of the British Anti War Movement to Iraq, Anas Altikriti, had actually made an appeal for the extension of the deadline in an interview with the Canadian Broadcasting Corporation (CBC) earlier yesterday afternoon and a similar plea on a local Iraqi station shortly after.
"Having arrived in Jordan to talk to parties and individuals who may have some influence upon or knowledge of the abductors, Mr Altikriti has stated that he is prepared to return to Iraq should that be in the best interest of the effort to secure of Mr Kember and his fellow hostages."
Yesterday Abu Qatada, one of Britain's most high-profile terror suspects, made a televised appeal for the release of Mr Kember.
Qatada, who has been described as Osama bin Laden's spiritual ambassador in Europe, was allowed to record the appeal inside Full Sutton maximum security jail, near York.
Today Maureen Jack, a member of the Christian Peacemaker Team who has spent time in Iraq, said it was hard to know whether to be hopeful about all the latest developments.
She said: "Obviously what would be more hopeful would be if there were signs of one or more of the hostages being returned to their families.
"It is difficult to know what to make of the extension of the deadline."She added: "I think the one thing that has been striking is the number of messages of support from people across the world including Muslim leaders, not just in Iraq but also in Palestine.
"That can only be helpful in securing the safe return home of the people who are missing."
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