The militants have released videos of the captives, including one - broadcast on Dubai-based TV station Al-Arabiya - warning that a hostage would be killed unless British troops withdrew from Iraq.
But the latest video gave Mr Moore's stepmother Pauline Sweeney cause to be positive.
"He looked a lot, lot healthier," she said, compared to "distressing" earlier footage.
Mr Moore had been working for American management consultancy Bearingpoint when he was kidnapped, while the other men were contractors employed to guard him.
In the latest video, released in March, he spoke in the plural which indicated the captives were being held together and not separately as previously thought, Mrs Sweeney said.
This also gave new hope to the mother of one of the kidnapped contractors who was last year reported to have committed suicide.
Meanwhile, the BBC has been shown a letter from the daughter of another of the guards - known only as Jason - to her father.
"We all want you to come home. I love you very much," wrote seven-year-old Maddi.
In a statement ahead of Friday's anniversary of the men's abduction, Mr Miliband backed the families' humanitarian appeals.
He said he was "totally committed" to working for the release of the men.
"I don't think that any of us can imagine their ordeal nor the anguish that their families and friends have had to suffer during this dreadful time.
"Our thoughts are with them all as they continue to endure the pain of being separated from their loved ones."
BBC security correspondent Frank Gardner said a deal with the captors had been "tantalisingly close" earlier this year.
But he added: "Progress has been delayed by a recent spike in violence. Most people believe this could still be a long drawn-out affair."
In his statement, Mr Miliband insisted the government was "totally committed" to working with Iraqi authorities and other allies for the safe release of the men.
He added that Iraq today is different to two years ago and there are "signs of progress and reconciliation".
"We call on those holding all hostages to release them immediately and unconditionally and return them safely to their families where they belong," he said.
Iraq national security adviser Mowaffak al-Rubaie: "It's very possible to get them back"
Former Beirut hostage Terry Waite, who spent almost five years in captivity in Lebanon, said that "hope must be kept alive".
"I can understand that at the time of an anniversary the feelings in the families run higher and higher, particularly as the time goes on," he told BBC Radio 4's Today programme.
"The one thing I would say to the families is maintain hope, keep hope alive."
He added: "If the hostages have the good fortune to be able to listen to this broadcast, as we did occasionally when we were in captivity... I would say: keep your hope alive.
"Many people are thinking of you, and we all sincerely hope you will be through this ordeal very quickly."
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