Stuart Steinberg, whose family lives in the San Fernando Valley in California, said his son was a sharpshooter for the Golani Brigade. The family left Monday for Israel, where their son will be buried.
The Jewish Journal was first to report his death.
Carmeli, 21, a sergeant, was from South Padre Island, Texas, said Maya Kadosh, deputy consul general of Israel to the Southwest.
He moved to Israel four years ago and joined the Israeli army after finishing high school there. He was also part of the Golani Brigade, said Rabbi Asher Hecht of Chabad of the Rio Grande Valley, a longtime family friend.
"He had great energy, yet had a kind and gentle soul," Hecht said. "We lost a gem."
Carmeli was the youngest of three children in the family and has two sisters who live in Israel. He had been living in Ra'anana, Israel.
More than 18,000 people from across Israel showed up Monday for Carmeli's funeral in Haifa, police said.
Carmeli was a fan of the Maccabi Haifa soccer team, and a team member — after learning Carmeli had no family living in Israel — sent a Facebook message to fans urging them to attend the funeral.
Steinberg was living in Beersheba, Israel, and had attended Pierce College and El Camino Real High School in California.
He visited Israel for the first time on a Birthright Israel trip with his younger brother and sister in June 2012, his father said. When he returned, he told his family that he was planning to return and join the Israel Defense Forces. He made good on that promise less than six months later, making the move in December.
"He went back," Stuart Steinberg said. "He was completely dedicated and committed to serving the country of Israel. He was focused, he was clear in what the mission was, and he was dedicated to the work he needed to be doing."
On Sunday, the Steinbergs were visited by representatives from the Consulate General of Israel in Los Angeles and told about the death.
"They're a very strong family but they're obviously dealing with a tremendous tragedy," Siegel said.
Max Steinberg "made a commitment to the state of Israel ... to really defend the civilized world against the threat of Islamic terrorism," Siegel said.