The Foreign Ministry said in a statement that the owner of the hijacked tug boat and coal barge has received two telephone calls, purportedly from the militant group Abu Sayyaf, demanding a ransom.
It said it was unclear when the incident occurred but that the ship owner was first contacted on Saturday. The ministry referred to the hostage-takers as pirates.
Foreign Minister Retno Marsudi told a news conference that she is working with Indonesian and Philippine officials to coordinate a rescue.
"Our priority is the safety of 10 Indonesian nationals who are now still in the hands of the hostage-takers," she said.
Abu Sayyaf, which is on U.S. and Philippine lists of terrorist organizations, is notorious for bombings, extortions and kidnappings for ransom in the volatile south of the Philippines. It has been weakened by years of U.S.-backed Philippine offensives but remains a security threat.
If the Abu Sayyaf is confirmed responsible, the number of hostages would be among the largest it has seized since 2001.
In the Philippines, army Maj. Gen. Demy Tejares said troops were trying to verify reports that the Indonesians were taken to the southern province of Sulu and that an Abu Sayyaf commander notorious for ransom kidnappings, Alhabsi Misaya, was involved.
"There is information pointing to Sulu as the destination so we're monitoring it," Tejares said of the predominantly Muslim province 590 miles (950 kilometers) south of Manila, where several other kidnapping victims are believed to be held by Abu Sayyaf militants.
Philippine military chief Gen. Hernando Iriberri flew to Sulu on Monday to meet commanders and their troops involved in efforts to locate the Indonesians.
The tug, Brahma 12, and the Anand 12 barge were going from Sungai Putting in Kalimantan, which is the Indonesian part of Borneo island, to Batangas province, south of the Philippine capital.
The Facebook page of the Brahma 12's captain, Peter Tonsen Barahama, shows smiling photos of him and the crew on the vessel preparing for the voyage and good luck wishes from friends commenting on a port clearance document he posted. The document shows the vessel and its barge left a port in southern Kalimantan on March 15.
A Philippine police report said a villager sighted an unmanned boat marked "Brahma 12" on Saturday drifting in waters off Languyan town in the southernmost Philippine province of Tawi Tawi, near Sulu, and the vessel was taken by police to a Languyan wharf.
Indonesia's Foreign Ministry said it believes the barge, carrying about 7,000 tons of coal, is still under the control of the hostage-takers.
Philippine security officials suspect the Abu Sayyaf was responsible for last year's abductions of two Canadians, a Norwegian and a Filipino woman from a marina on southern Samal Island. The victims are believed to be held in the jungles of southern Sulu province.
In a recent video posted on a Facebook account linked to the militants, they threatened to kill the hostages unless a large ransom is paid by April 8. The Philippine military said the government continues to observe a no-ransom policy.
Indonesia has been helping the Philippines forge a peace agreement with Filipino Muslim rebels by sending soldiers to join an international group that helps monitor government and rebel adherence to a cease-fire.
© 2016 The Associated Press.
