Rescue workers at the site of the crash on Java Island early on Saturday were checking whether more bodies or injured passengers remained trapped in the wreckage of the trains, which were carrying a total of 1,000 passengers, said local railway official Sarni, who like many Indonesians goes by one name.
Officials were investigating the cause of the accident at Gubuk station, but Sarni told AP that it appeared the moving train had time to break before it smashed into the stationary one.
Both trains were bound for Surabaya, Indonesia's second city, a police official told Reuters.
One of the train drivers was among the dead, he said.
Aging railway network
The accident occurred just after 2am, said Sarni.
One of the train drivers is said to
be among the dead
He said 13 people were killed and 26 others were injured.
Djoko Susilo, a nurse at a nearby hospital, earlier said 11 bodies had arrived at his hospital.
Gubuk is about 450km east of the capital, Jakarta.
Train accidents are common on Indonesia's aging railway network, especially at crossings.
Last year, a family of 12 was killed when a train crashed into a minibus on Java, and on average dozens die each year in similar accidents.