Another shows a group with a sign that reads, "Please try to understand our painful life New Zealand Government and save our life. Please".
A letter, written in both English and Tamil, said it was unsafe for the group's members to return to their home countries of Sri Lanka, Bangladesh and Burma.
It states that the group left Indonesia on May 5 and travelled for 12 days before encountering Australian officials. After confirming they were not attempting to enter Australia, the group were allowed to continue, the letter states.
A short time later the asylum-seekers were turned around by Australian authorities, after being transferred to two smaller boats, the group's letter states.
When a boat hit rocks near an Indonesia island, "we jump over the boat to sea and swim more than one and a half hours [to] reach island".
A spokeswoman for Immigration Minister Michael Woodhouse said to her knowledge the Government had not yet received the letter, and the group could not claim asylum without being in New Zealand.
"As it was the Australian authorities who responded to the distress call and boarded the ship, any queries should be directed to them."
Labour leader Andrew Little said authorities should investigate whether the group were genuine refugees, and if so, consider processing them as part of New Zealand's quota.
Destination NZ
• A plea for help has apparently been made to the New Zealand Government by a group of 65 asylum-seekers.
• The group were intercepted by the Australian Navy and their boat later crashed on to rocks off a remote Indonesian island.
• They have said their destination was New Zealand.