Australian foreign minister Alexander Downer says the government’s emergency response team has not found any new information on his location.
It’s believed the 63 year-old engineer was taken hostage 48 hours before his captors released a DVD on Monday.
The video shows Mr Wood pleading for his life and urging foreign troops to leave Iraq.
On Wednesday his brothers Malcolm and Vernon recorded an emotional plea for broadcast on Arab television, including the Al Jazeera network.
“We are extremely concerned for Douglas’ welfare,” Malcolm Wood said in the message.
“He has a serious heart condition. In his current stressed environment, without his medication, his health could fail him altogether.”
“In fact, without his medication he may be unable to comply with all of the demands made of him.”
Malcolm Wood argued his brother’s captivity would do nothing to change the Australian government’s policy on Iraq.
Mr Wood said in the appeal his brother had been working on civil projects to improve the lives of local people in Europe and the Middle East.
But he said if the captors released him, his family would ask him to end his work in Iraq.
Douglas Wood, an Australian citizen who has lived in the US for the past decade, has a wife and several children and is a grandfather.
Mr Downer made his own public appeal on Arab television.
He says the government’s taskforce is working with Iraq’s government and a number of countries, including the US, the UK Turkey and France, to secure Mr Wood’s release.
He said that as some of these countries have experience with hostages in Iraq, it’s hoped they can pass on information and give Australia leads to follow.
Read the full text of the Wood family’s appeal