The capacity for secret key agreement for permutation-invariant and symmetric sources under a sampling attack is investigated. The supremum of the normalized secret key capacity is introduced, where the supremum is taken over all permutation-invariant sources or all symmetric sources and the normalized secret key capacity is the secret key capacity divided by the description length of the symbol. It is proved that the supremum of the normalized secret key capacity bound under a sampling attack is close to 1/m for permutation-invariant sources and O(1/m) for symmetric sources, where and m is the number of Eve's sources