In a statement released by the National Conference, Omar, who is also its working President, said that Mehbooba was "evidently terrified" and "petrified" of facing the people.
"In seeking the postponement of the election for the Anantnag assembly seat, Mehbooba Mufti has shown that she has panicked and is hiding behind the Election Commission.
"This desperate and evasive move shows how badly the Chief Minister is governing the state and is a formal admission of defeat by the PDP-BJP alliance," he said.
He said Mehbooba was trying to escape the consequences of PDP's sell-outs and political surrenders under the fig-leaf of an allegedly 'non-conducive' situation.
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"When the Chief Minister is petrified of failing to seek an electoral validation to continue in her chair, the very credibility, mandate and writ of the Government becomes questionable.
"Knowing well that her party is facing a complete rout at the grassroots level, Mehbooba has chosen to run away from her very first test and that's tragic," he said.
"Mehbooba's spectacular U-turn on seeking Confidence Building Measures (CBMs) from the Government has catalysed PDP's political obliteration. If she is so scared of facing the people, with what credibility and confidence will she rule the state?", he asked.
Earlier Omar had tweeted saying the postponement of bypolls admission of "how bad things have become under @mehbooba_mufti and how petrified she is of facing the people in the by-election."
Located in South Kashmir, Anantnag seat fell vacant after the death of the then state Chief Minister Mufti Mohammed Sayeed on January 7.
The EC said in a statement that the Chief Secretary apprised it that the law and order situation of Anantnag district "due to certain recent incidents is not conducive at the moment for the holding bye-election".
The Commission had announced bypoll to this seat along with eight other assembly seats on May 16.
The poll panel today said that fresh date will be announced later.