Two men from Taiwan's outlying Kinmen island were found on March 18 by the coastguard of China's Fujian province after the engine of their boat failed.

Chinese authorities said one of the anglers, surnamed Hu, was an active member of Taiwan's military, accusing him of intentionally concealing his identity.

Taiwan's defence ministry confirmed Saturday that Hu was part of Kinmen Garrison Brigade.

"(He) went fishing during his vacation and lost contact due to heavy fog. He contacted his family and service unit that he was rescued by the Chinese coast guard and is safe," said Kinmen's Defence Command in a statement.

It added that they were cooperating with other agencies and hoped "for the safe return of its personnel to Kinmen as soon as possible on humanitarian grounds".

Kinmen Defence Command also said it will tell soldiers "to refrain from participating in various risky activities during their vacation".

The other man in the fishing boat, surnamed Wu, was repatriated to Kinmen by Taiwan's coast guard on Saturday.

According to video footage shared by Kinmen lawmaker Chen Yu-jen -- who was at the dock -- he was greeted by his tearful mother with a hug when he stepped off the boat.

Hu's mother told reporters that she hoped China would allow family members to go visit him.

"Our hearts are filled with anxiety when we can't see him in person, although my son has sent a message saying he is safe," she said.

China's Taiwan Affairs Office -- a mainland body tasked with handling cross-strait relations -- had told Chinese state news agency Xinhua that Hu needed to be held "to further verify and understand the situation".

China claims self-ruled Taiwan as part of its territory, and has said it will not rule out force to bring the island under Beijing's control.

This incident comes in the wake of an ongoing row between Taipei and Beijing over a fatal boat incident last month.

A Chinese speedboat carrying four people capsized on February 14 near Kinmen while Taiwan's coast guard was pursuing it, leaving two dead.

The coast guard had defended its actions, saying the boat was within "prohibited waters" and was zigzagging before it capsized, but Beijing has accused Taipei of "hiding the truth" about the incident.

Since then, China said it would step up patrols around Kinmen -- a territory administered by Taipei but located just just five kilometres (three miles) from the mainland city of Xiamen.