The Westboro Baptist Church regularly pickets military funerals, saying American soldiers are dying overseas because God is displeased that the US tolerates homosexuals.
But the group issued a statement today saying a representative will appear on a nationally syndicated radio talk show instead.
Pennsylvania Governor Ed Rendell had already appealed to the group to allow the Amish to conduct their funerals in privacy.
In a statement on its website, the church blamed Rendell for the deaths of the Amish children because of comments he made about the Westboro group on national television several months ago.
"They're insane," Governor Rendell responded when asked about the group's statement.
In June, Governor Rendell signed legislation designed to restrict the group by making it a crime to demonstrate within 150 metres of a funeral or memorial service in Pennsylvania.
Funerals private
State police will provide security at the Amish funerals to keep reporters, the public and any potential demonstrators at a respectful distance from mourners.
The Federal Aviation Administration also will keep aircraft, such as media helicopters, at least four kilometres away, although a single helicopter may pool television coverage if the Amish approve.
"We're trying to look at every possible precaution available with the ultimate goal of allowing these people to mourn as we would want to if this happened to our family," said Kate Philips, Governor Rendell's press secretary.
On Monday morning, Charles Carl Roberts entered the West Nickel Mines Amish School in Lancaster County and shot 10 girls execution style, killing five of them. He then killed himself as police stormed the building.