It says the Nauru government has refused the group's visit request because it is an incredibly busy time, despite Amnesty offering alternative dates.
Earlier this month, a team of United Nations human rights observers was denied entry.
None of the asylum seekers have been advised if they have secured refugee status.
A new human rights report by a Melbourne University says Australia's asylum seeker policies and practices are in breach of at least seven international laws.
The latest refusal of access comes just days after reports of children being abused at the camp at the hands of guards.
Nauru tightened media access in January by hiking a non-refundable journalist visa application fee by 4,000 percent.