The group had called for the strike tomorrow to protest the death sentence handed down to Jamaat chief Motiur Rahman Nizami, Barua and 12 others in a 2004 arms smuggling case.
Jamaat leader Shafiqur Rahman said in a statement the party would observe a "peaceful" agitation across Bangladesh tomorrow. The strike was put off till Thursday.
The second phase of the Bishwa Ijtima, the second largest Muslim congregation in the world, will end on Sunday while Saraswati Puja falls on Tuesday.
Besides the Jamaat chief, Bangladesh Nationalist Party (BNP) leader and former minister Lutfozzaman Babar and two retired army generals who headed intelligence agencies were also sentenced to death.
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Yesterday, Jamaat claimed the government was "plotting to kill" Nizami. It dubbed the arms haul cases "false and unfounded" and called the trial a "farce" and "politically motivated".
The main opposition BNP described the tribunal's verdict as a "deep conspiracy" to ruin it.
Around 1,500 boxes containing submachine guns, AK-47 assault rifles, submachine carbines, Chinese pistols, 840 rocket launchers, 27,000 grenades and 11.41 million bullets were seized from 10 trucks in the early hours of April 2, 2004.