“They were kidnapped by Hamas terrorists and are being held hostage in Gaza,” the statement read.
Mollel’s father told the BBC he has hope that his eldest son will return safely.
He said that Tanzania’s ambassador to Israel had assured him the two governments were working together to secure their release.
Before it was confirmed that his son, 21, had been taken hostage, Mr Mollel told the BBC he couldn’t eat or sleep because he was desperate to know what had happened to him.
“When I go to the market people ask me why I’m losing so much weight,” he said last week.
The last time Mr Mollel spoke to his son was on Thursday 5 October – two days before the Hamas gunmen attacked Kibbutz Nahal Oz, where he was studying.
The last words he said were: “Be on your best behaviour because you’re somewhere new, and make the most of the internship you’re there to do.”
Mr Mtenga’s family is yet to speak publicly.
They were among 260 Tanzanian students in Israel.
On 7 October 1,400 people were massacred by Hamas – which the UK, US and other Western powers class as a terrorist organisation – in Israel.
More than 220 hostages were taken over the border to the Gaza Strip which is under control by the barbarian Hamas.
Israel says they come from 25 countries, including one South African who is yet to be identified. The South African authorities have not commented.
