"We can't confirm it has crashed. We can say contact has been lost with the plane," BASARNAS chief Bambang Soelystyo told Reuters by phone.
"It's a Trigana airline plane carrying 54 people including 5 crew. We are working to get more details."
According to the official BASARNAS Twitter account, the aircraft, a short-haul ATR 42-300 airliner belonging to Trigana Air Service and built in France and Italy, was carrying 44 adult passengers, five crew and five children and infants.
The plane was flying between Jayapura's Sentani Airport and Oksibil, due south of Jayapura, the capital of Papua province.
The agency's Jayapura office was coordinating the search, a separate tweet read as dusk set in in the tropics.
Air transport is commonly used in Papua, Indonesia's easternmost province, where land travel is often impossible.
It was not immediately clear if search efforts would continue into the night in the densely forested mountainous region where the aircraft was travelling.
According to the Aviation Safety Network, an online database, the ATR 42-300 had its first flight 27 years ago. ATR is a joint venture between Airbus and Alenia Aermacchi, a subsidiary of Italian aerospace firm Finmeccanica .
Trigana has been on the EU blacklist of banned carriers since 2007. Airlines on the list are barred from operating in European airspace due to either concerns about its safety standards, or concerns about the regulatory environment in its country of registration.
The airline has a fleet of 14 aircraft, according to the airfleets.com database. These include 10 ATR aircraft and four Boeing 737 classics. These have an average age of 26.6 years, according to the database.
Trigana has had 14 serious incidents since it began operations in 1991, according to the Aviation Safety Network's online database. Excluding this latest incident, it has written off 10 aircraft.
Indonesia has a patchy aviation safety record and has seen two major plane crashes in the past year, including an AirAsia flight that went down in the Java Sea, killing all on board.
That crash prompted the government to introduce regulations aimed at improving safety.
Indonesia's president promised a review of the ageing air force fleet in July after a military transport plane crashed in the north of the country, killing more than 100 people.