Israel would not have agreed to the prisoner swap that freed a hostage had the true circumstances of his capture been known, according to media reports.
Shin Bet say Tannenbaum's story does not make sense
Elhanan Tannenbaum was the only living captive given to Israel last month in exchange for about 400 Palestinians and 59 dead fighters, mostly of Hezbollah.
But Channel One said he was not fully co-operating with interrogators who doubted his story about his capture.
Israeli media reported earlier that Mr Tannenbaum failed lie-detector tests.
Israeli lawmakers also expressed concerns that Mr Tannenbaum - a businessman and a reservist colonel, may not be telling the truth about his capture - reportedly in October 2000.
But his son said Israeli legislators had defamed Mr Tannenbaum.
Last month, the militant group Hezbollah also handed over three dead Israeli soldiers that were killed in Lebanon in 2000.
The agreement came after three years of German-led negotiations.
Mr Tannenbaum reportedly said he had been taken to Beirut by force from a Gulf city - apparently Dubai - where he had travelled from Belgium.
Israeli businessman Elhanan Tannenbaum
Remains of three Israeli soldiers
400 Palestinian prisoners
About 30 Arab fighters, 23 Lebanese
Remains of 59 militants
But Avi Dichter, the head of Israel's Shin Bet domestic security service, told Israeli legislators that investigators doubted Mr Tannenbaum's story.
An unnamed Knesset security committee member told the Israeli daily Haaretz that the Shin Bet considered Mr Tannenbaum's testimony illogical.
And the committee member quoted Mr Dichter as saying that Mr Tannenbaum had failed a lie-detector test when asked what he had told his captors about his military record.
On Wednesday, the committee took the unusual step of issuing a statement describing the Tannenbaum affair as "one of the most serious and worrisome known to Israel," Israeli newspapers reported.
The statement said the committee would not be satisfied until all circumstances were clarified, the damage to state security established and the necessary measures taken.
In response, Mr Tannenbaum's lawyers said it was wrong for the committee to "take a stand during an ongoing investigation and turn itself into a judiciary that passes judgment on a person being interrogated," according to Haaretz.
Investigators have been questioning Mr Tannenbaum since he returned to Israel last month.
Israel Army Radio said on Thursday that indictments could be filed against him.
On Tuesday, a court remanded him in custody for 10 days.
Hezbollah had accused Mr Tannenbaum of being a spy for Israel and said it had lured him to Lebanon believing he was going to penetrate the organisation.