"As of Monday noon, we received information that the Indonesian boat crews are in good condition," China's Xinhua news agency quoted Indonesian Foreign Affairs Minister Retno L.P. Marsudi as saying in a statement.
The Indonesian hostages were not on the Basilan Island in southern Philippines during the nine-hour gunfight on Saturday, which killed 18 Philippine soldiers and five Abu Sayyaf militants.
The Indonesian government has been stepping up efforts to rescue the kidnapped seamen of the Indonesian-flagged tugboat Adnan 12 since the vessel was hijacked by the rebels while it was en-route to the Philippines from Banjarmasin, South Kalimantan which is the Indonesian part of Borneo island.
"We will continue to intensify our communications with the Philippine authorities, and our coordination with related institutions in Indonesia," Retno said.
The 10 sailors have been held hostage since March 25 by the militant group.
The Abu Sayyaf group, which has long been notorious for carrying out kidnappings, beheadings, bombings and extortion, demanded a ransom of an equal US$1.1 million from the company that owned the vessel for the release of the crew members.
Retno said that the government would not pay the ransom.
"The Indonesian president and vice president are paying close attention to the rescue efforts, and have instructed to strengthen coordination," he said.