Habibullah Mir, who was affiliated with the Congress, was shot in the neck by the unidentified militants at his home in Goripora village, 52 kms from here, at around 12.20 pm, a police spokesman said.
Mir was rushed to a sub-district hospital where he subsequently died, the spokesman said.
This is the first attack on a panchayat member by militants this year. Several Sarpanches and Panchayat members had been targeted by suspected militants in the border state since 2011.
Omar, who was in Pune, said it was necessary to step up security of Panchayat heads who have come under attack from suspected militants in the state.
"One more Sarpanch was killed today. It is necessary to step up security measures to protect the Sarpanches in the state," he said.
Omar was talking to reporters on the sidelines of a "Students' Parliament" organised by Maharashtra Institute of Technology (MIT) here.
The National Conference leader said it was not yet clear as to which elements were behind the act.
Earlier, addressing the student delegates at MIT, Abdullah said the youths of Jammu and Kashmir had grown up in the "shadow of gun" and were angry because political issues in the state were still unresolved.
He said the people of his state, who had been struggling against militancy, wanted to come out of the "darkness" and see the youths getting job opportunities with the investments of big companies in Jammu and Kashmir.
He urged the students not to hate politics but ensure removal of bad politicians from power by exercising their democratic right of voting.
"India has an unblemished record of democracy and the average turn out of voters in recent elections had gone up," the 42-year-old Chief Minister added.
