In the weeks before their family trip to Costa Rica, Bruce and Irene Steinberg of Scarsdsale, N.Y., told friends and family how excited they were to take their three sons on an adventure through that country’s lush forests and tropical beaches.

After visiting the Pacific coast, the Steinbergs were headed on Sunday to Costa Rica’s capital for the last stop of their trip. But the single-engine plane carrying the Steinbergs — along with four members of another family, the Weisses from Belleair, Fla., as well as a 10th American passenger and two Costa Rican crew members — crashed that afternoon into a mountain shortly after takeoff, killing everyone on board, the authorities said.

Officials in Guanacaste, a popular region on the Pacific coast for tourists, responded to reports shortly after noon of smoke and flames rising from a wooded area near Punta Islita Airport. Emergency responders found the charred wreckage of a Cessna plane operated by the regional airline Nature Air and the burned remains of those who had been on board.

“The government of Costa Rica deeply regrets the death of 10 American passengers and two Costa Rican pilots in the aircraft crash,” Luis Guillermo Solís Rivera, the country’s president, said in a Facebook post on Sunday evening.