Ms Taylor's family welcomed the UN call for her to be freed from a Libyan jail.
She and three colleagues from the International Criminal Court have been accused of smuggling documents to the son of deposed leader Muammar Gaddafi.
The 15-member Security Council issued a statement calling for the group to be freed immediately.
The former Brisbane woman's sister Danielle Taylor says the UN's involvement is positive news.
"We're extremely happy with all the support that we've got and obviously having the backing . . . obviously adds a lot more strength to trying to get Melinda released," sjhe said.
John and Janelle Taylor say they now realise realise it may be some time before their daughter is released from prison in Libya.
Australian ambassador David Ritchie has met Ms Taylor and her three International Criminal Court (ICC) colleagues, who were detained last week while interviewing Saif al-Islam Gaddafi.
Mr Ritchie told Ms Taylor's parents he now knows the matter will not be resolved in the short term.
Mr Taylor says they have had a hard time since learning a week ago their daughter had been detained.
"We've been a little bit fragile because we don't know what's happening," Mr Taylor said.