One of the soldiers was in critical condition after Hezbollah launched its cross-border attack July 12, while the other was seriously wounded, the officials said, speaking on condition of anonymity under military rules. Military censors had previously prohibited publication of their conditions.
Hezbollah has not released any details on the conditions of Eldad Regev and Ehud Goldwasser or provided any signs that they are still alive.
Israeli Prime Minister Ehud Olmert hinted this week that they might be dead, reports CBS News correspondent Robert Berger, which angered family members.
"We have been informed that they have been wounded, but we are acting on the assumption that they are alive," Shlomo Goldwasser, the father of one of the kidnapped soldiers, said.
In other developments:
Hezbollah has demanded that Israel release Arab prisoners in exchange for the missing servicemen. Olmert has demanded that Hezbollah provide signs of life before he will consider a deal.
In a statement, the military would say only that a report about the circumstances of the abduction has been given to the defense minister, army commander and families of the soldiers.
"The working assumption of the army was and remains that the abducted soldiers are alive and according to that assumption the army continues its efforts to bring the soldiers home," the statement said.
Three soldiers were killed in the attack, and it was widely believed that the two captured soldiers were wounded after a fierce battle at the scene. But the military was unsure of their conditions until it completed an investigation several weeks after the incident.
The attack sparked a 34-day war between Israel and Hezbollah. More than 1,000 people were killed on both sides, according to the U.N. and Israeli and Lebanese officials.
Lebanon says most of those killed were civilians. Israel claims 800 Hezbollah fighters were killed, though that figure was not substantiated. On the Israeli side, 159 people were killed, including 39 soldiers.
The U.N.-brokered cease-fire that ended the war calls for the unconditional release of the soldiers. Under the cease-fire, a beefed-up U.N. peacekeeping force, along with Lebanese government troops, is policing the border with Israel.
A third soldier, Gilad Shalit, was captured 17 days earlier by Palestinian militants, and is still being held, reports Berger. However, he is known to be alive and in good condition. Hamas has demanded 1,400 Palestinian prisoners, including top militants, in exchange for the 19-year old corporal.