Haussmann's partner Sarah Watson, clutching their son Theo, said the activists were good people.
"These are not crazy nut-bars, they're normal peaceful people ... and they believe in the right to peaceful protest and the right of free speech and I believe they deserve some support from everybody and that includes the New Zealand Government."
Beauchamp's niece Zara Mansoor read a letter written by her grandmother, Mary Beauchamp, about her son.
The letter said: "Our John is a caring, piratical, commonsense sort of man and very brave too.
"He is particularly passionate about the Arctic, the ocean and all the creatures that depend on this environment."
Amnesty International spokeswoman Lara Rapson condemned the piracy charges as having no basis in law "or reality" and called for them to be dropped.
Greenpeace New Zealand board chairwoman Stephanie Mills said the New Zealanders were coping well, but it was a difficult time for their families.
Lawyers for the environment group have lodged formal appeals in the Murmansk Lenin district court against the continued detention of the crew members, who have been dubbed "the Arctic 30".
- Additional reporting, AP