A spokeswoman for the US embassy in Dublin last night said the country respected the decision of the court in relation to the Blake's case, but said any decision on whether to appeal was up to the relevant US and Irish judicial authorities.
"We appreciate the hard work of the Irish Government officials and of the court in dealing with the facts of the case, which arise from a difficult child custody matter," the embassy said.
"The decision on whether or not to appeal today's decision is one that is left up to the relevant US and Irish judicial authorities."
Solicitor for the Blakes, Don Ryan, said that his clients, who were accompanied to yesterday's hearing by their son, John, were very relieved at the court's decision and were grateful to Mr Justice Michael Peart for giving them a very fair hearing.
Mr Ryan said they were delighted to be returning to Cobh to be back with their family.
"They are very happy and very satisfied with what happened this morning . . . It's been a tough year or so for them. They got quite a shock when they were arrested out of the blue in September 2005 and were taken to Dublin.They were in custody for several hours until we could get bail for them and that was very stressful for them," Mr Ryan said.
"Over the past year, there have been several other trips to Dublin for them - now the court has been good in not bringing them up every time, but the hearing two weeks ago and today were two days they certainly wouldn't want to go through again.
"They had no idea what was going to happen today and I suppose they were quite worried that they were going to be extradited, but we had to reassure them that they would get a fair hearing from the court and that's what they got, and they're delighted.
"We have no idea what the American authorities are going to do now - whether they're going to appeal today's decision - that's out of our hands. But Tim and Ethel just hope that this is the end of the matter and they can get on with their lives back in Cobh," he added.
The Blakes's daughter, Serena Benwell, who wrote to both the Irish and the American authorities, asking them not to go ahead with her parents extradition, could not be contacted by The Irish Times for comment last night.