Investigators are working into what caused a charter aircraft carrying 10 US citizens and two local crew members to crash in a wooded area in Costa Rica, killing everyone on board.

Officials said they were still seeking to establish the names of the Americans who died when the plane went down at midday on Sunday in Guanacaste.

They said Nature Air - who owned the plane - had provided a passenger list, but the names on it had not been confirmed.

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A family in the suburbs of New York City said five of the dead Americans were relatives on holiday.

They identified them as Bruce and Irene Steinberg and their sons Matthew, William and Zachary, all of Scarsdale.

"We are in utter shock and disbelief right now," Bruce Steinberg's sister, Tamara Steinberg Jacobson, wrote on Facebook.

Rabbi Jonathan Blake of the Westchester Reform Temple in Scarsdale said in a statement posted on the Temple's Facebook page that the Steinbergs were involved in philanthropy and local Jewish groups.

"This tragedy hits our community very hard," Mr Blake wrote.

At a news conference, Enio Cubillo, director of Costa Rica Civil Aviation, said the Nature Air charter flight crashed shortly after taking off just after noon on Sunday from Punta Islita on a planned flight to the capital of San Jose.

He said investigators were looking into possible causes.

Mr Cubillo identified the pilot as Juan Manuel Retana and described him as very experienced.

Former Costa Rican President Laura Chinchilla said via Twitter that Retana was her cousin.

The same plane had arrived in Punta Islita on Sunday morning from San Jose and was delayed in landing by strong winds, Mr Cubillo said.

Nature Air did not respond to phone and email messages.