Tannenbaum, a colonel in the Israeli army reserves, was captured by the Lebanese resistance group Hizb Allah in October 2000. Israel described him as a businessman, but Hizb Allah insisted he was a spy.
"The committee demands that security and judicial bodies put at the disposal of investigators (interrogating Elhanan Tannenbaum) all means to reach the truth in this affair, which could turn out to be the most threatening and serious in Israel's history," said a statement on Wednesday by an Israeli parliamentary committee, which deals with intelligence matters.
Israeli public radio said the committee's deliberations are normally kept secret, making the publication of the statement
The committee in charge of intelligence and Israel's secret services - a subcommittee of the powerful defence and foreign affairs committee - said it had "followed with interest" the Tannenbaum case.
"The committee will not rest and will not stay silent until light has been shed on all aspects of this affair, including the reason why he ended up in Lebanon and the (subsequent) damage for state security," the committee said, without further clarification.
Businessman or a spy?
"The committee will not rest and will not stay silent until light has been shed on all aspects of this affair, including the reason why he ended up in Lebanon and the (subsequent) damage for state security."
Tannenbaum was released as part of a major German-brokered prisoner swap last month, in which Israel freed nearly 450 prisoners, most of them Palestinians and Arabs, in exchange for Tannenbaum and the bodies of three soldiers.
Since returning to Israel, the businessman has been interrogated by investigators at a police station.
On Tuesday, at the request of investigators, a Tel Aviv district court granted police 10 extra days to question Tannenbaum, court sources said.
The circumstances of Tannenbaum's apprehension are still unclear.
Some press reports say he was captured by Hizb Allah while trying to conclude a deal to wipe out his gambling debts. Other reports say, as a reserve colonel, he had access to sensitive information.