TAIPEI—Taiwan submitted to be part of a trans-Pacific trade team, times right after China formally submitted its application, possibly compounding an by now uncomfortable place for the pact’s 11 customers.

Lo Ping-Cheng, a cupboard spokesman for the self-governing island, which China considers as element of its territory, reported on Wednesday that Taiwan has notified all customers of the Extensive and Progressive Arrangement for Trans-Pacific Partnership, regarded as the TPP, of its official application to be part of and sought their assist.