The assault on Falluja, which began on 8 November and has in recent days witnessed renewed fighting, left at least 71 US military dead, according to the families, and the Iraqi government said more than 2000 Iraqis were killed.
It is unknown how many of the 2000 were civilians.
"This delegation is a way for me to express my sympathy and support for the Iraqi people," said Rosa Suarez of Escondido in California.
"The Iraq war took away my son's life, and it has taken away the lives of so many innocent Iraqis. It is time to stop the killing and to help the children of Iraq," she added in a statement released by the families.
The families said with peace groups, physicians' organisations and relatives of the 11 September 2001 attacks' victims, they raised 100,000 dollars in an internet appeal. Humanitarian groups such as Middle East Children's Alliance and Operation USA contributed 500,000 dollars worth of medical supplies.
The families are to fly to Amman on 26 December and hand over the supplies to humanitarian and medical workers there.