Westchester Reform Temple confirmed that Bruce and Irene Steinberg and their sons, Zachary, William, and Matthew, were on the plane that carried a total of 10 U.S. citizens and two Costa Rican crewmembers.
"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," Blake wrote.
On Monday, Rabbi Jacob Luski of Congregation B'nai Israel in Saint Petersburg, Florida, said that relatives had informed him of the deaths of Mitchell and Leslie Weiss and their two children, 19-year-old Hannah and 16-year-old Ari.
Luski said both of the parents were doctors. The family lived in Belleair, along the Gulf of Mexico.
Enio Cubillo, director of Costa Rica Civil Aviation, said the Nature Air charter flight took off just after noon Sunday from Punta Islita and was headed for the capital of San Jose when it crashed in a wooded area.
He 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, Cubillo said.
Nature Air did not respond to phone and email messages.
The Associated Press contributed to this report.