Israel's military says it has accounted for all its troops after reports that a soldier had been kidnapped sparked a major security operation.
The military said no soldiers were missing after carrying out a roll-call.
Dozens of roadblocks were set up on Thursday after a female soldier said she saw another soldier being bundled into car near Ben Gurion airport.
A previously unknown Palestinian group calling itself the Al-Quds Army later said it had taken a soldier.
Israel already has one soldier being held captive, Sgt Gilad Shalit, who was captured by Hamas-linked militants three years ago.
"Following a testimony of a woman soldier who said that (she saw) two people pushing a soldier into a car, Israeli police and the Israeli army acted according to procedures," said police spokesman Alex Kagalsky on Thursday.
Ben Gurion airport is near the city of Tel Aviv in central Israel.
Police quickly set up roadblocks on major routes, causing severe traffic jams in some areas.
Egypt has been mediating in attempts to free Gilad Shalit
The Palestinian news agency Ma'an later on Thursday reported a statement from the Al-Quds groups, saying: "A group of our resistance fighters captured an Israeli soldier near Ben Gurion airport and withdrew along with the soldier peacefully - later we will give details about the captured soldier."
In June, Israel marked three years since Sgt Shalit, then aged 19, was seized by Palestinian militants in a cross-border raid launched from Gaza.
Indirect talks between Israel and Hamas, which controls the Gaza Strip, have so far failed to secure his release.