Two children were also killed on Monday during an exchange of gunfire between Indian and Pakistani troops, Indian authorities said.
Three members of this squad were also involved in August 26 Pulwama district police lines attack, in which eight security personnel were martyred.
The attackers breached four layers of security in the highly-protected zone which houses many of Jammu and Kashmir's Who's Who.
He said that: "JeM is a threat because the cadres believe in such kind of activities, like attacking the camps. The identity is yet to ascertained", Director General of Police SP Vaid said. Roads leading to the airport, which were sealed off earlier, have also reopened.
The terrorists, according to BSF officials are holed up inside the building campus of the 182nd Battalion camp.
#8:39 AM: Passengers now allowed to enter Srinagar Airport after security check to avoid inconvenience.
"While two militants were killed during the night operations only, a third militant continued to fire on the forces from inside the camp before he was killed in the afternoon", a senior police official said.
At 3:45am, fidayeen attackers entered the BSF camp located near the Srinagar worldwide airport, following which there was heavy exchange of gunfire. "Firing is ongoing", BSF officials added.
Schools in the vicinity of the airport have been closed.
He said that around 4.30 am, a group of terrorists presumably "fidayeen", attacked the 182 battalion camp of the BSF.
Singh said he has spoken to the chiefs of the Border Security Force and Central Reserve Police Force following the suicide attack near the Srinagar airport.
"I have spoken to the DG, CRPF, and DG, BSF".
Today's fidayeen attack is the 2nd high profile attack on the highly fortified security installation within a month in Kashmir Valley.