The Virgo Transport 8 ship carrying 243 people went missing in bad weather early on Sunday, the rescue agency said.
Authorities have since rescued 108 people from the ship, which was travelling from Surabaya in East Java to Banjarmasin in South Kalimantan.
Choppy waters with high waves and strong winds were impeding the search on Monday, said Mohammad Syafii, head of the national rescue agency.
The agency has deployed at least 622 personnel, 17 ships, five helicopters and aircraft to find the missing passengers, Syafii said.
Some of the ships have arrived at the location but it was difficult for rescuers to make their way into the capsized and partially submerged ship, he said.
"We would also deploy personnel with underwater rescue skills but the current conditions do not allow us to," he said.
"While waiting for the weather conditions to improve, we are identifying more personnel with special skills," he said, adding the death toll remained at six.
In a video shared by the rescue agency, a large red-and-black ship was capsized and partially submerged in choppy blue water, with its red-painted underside visible above the surface.
Two small boats, each carrying people, were seen floating in rough waters near the capsized ship.
The location of the capsized boat is almost 150km from the command centre at Trisakti Port in Banjarmasin, another official at the rescue agency told Reuters.
"The conditions there are quite windy, making it difficult for the (rescue) vessels to dock," the official, Arianto Ardi, said.
As of Monday afternoon, none of the 129 missing people had been found, Arianto said, adding that rescuers were still unable to conduct a search for the victims due to the weather.
The weather was very poor when the incident happened, with waves as high as three metres crashing into the ship, Syafii said.
It takes about five hours to reach the location from Trisakti Port in good weather but requires up to nine hours in rough conditions.
On Sunday, Edy Prakoso, another official at the agency, said the ship leaned heavily to one side after strong waves hit its starboard side.
Transport Minister Dudy Purwagandhi said the capsized boat had the capacity to contain 500 passengers, so it was not overloaded.
The incident took place in the Java Sea - the waters between Indonesia's four most populated islands of Java, Sumatra, Sulawesi and Borneo - has been the site of some of Indonesia's deadliest maritime disasters.
Indonesia relies on ferries across its 17,000 islands, with sea travel cheaper and more accessible than flying, but there have been numerous accidents.
In August, two passenger ferries caught fire in separate incidents, killing six people - five off Madura island and one on a route from the island of Bali.
with AP
