Fundamentalist Jamaat-e-Islami Secretary-General Ali Ahsan Mohammad Mujahid, 67, and BNP leader Salahuddin Quader Chowdhury, 66, were hanged at Dhaka Central Jail at 12.55 AM, a senior jail official who witnessed the execution told PTI.
President Abdul Hamid rejected their mercy petitions last evening, hours after they had sought presidential clemency in a last-ditch attempt to escape the gallows. The two men were the first war crimes convicts to seek presidential clemency.
The two men were "unflustered" during their execution, Detective Brach Deputy Commissioner Sheikh Nazmul Alam said.
"The duo were silent when they were being taken to the gallows. They did not react. The ropes were pulled simultaneously," he was quoted as saying in the media.
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Soon after the execution, ambulances escorted by elite anti-crime Rapid Action Battalion (RAB) and armed police came out of the prison complex carrying the bodies.
Chowdhury, a six-time MP and a former minister, was buried at the family graveyard at his ancestral home in Raujan's Gahira Village in Chittagong after a funeral prayer.
Mujahid, the second most senior member of Jamaat, was found to be a key mastermind of the massacre of the country's top intelligentsia just ahead of the December 16, 1971 independence war victory.
Jamaat, whose two other senior leaders already have been
executed on war crimes charges, issued a statement calling for a nationwide general strike tomorrow.
Bangladesh is on high alert and paramilitary border guards, RAB and police have beefed up the security across the major cities amid reports of violence from some places.
"Unknown miscreants attacked the microbus and opened gunfire. Rajib was shot. Others sustained minor injuries. The microbus' rear window was smashed," local media reports said.
On Wednesday, Bangladesh's Supreme Court upheld the death sentences against Chowdhury and Mujahid, who were convicted in 2013 on charges including genocide, rape and torture.
After news of their execution broke, supporters of Prime Minister Sheikh Hasina's Awami League and activists of Gonojagoron Mancha took to the streets to celebrate the executions and also unfurled national flags near the prison.
Intelligence agencies fear that the executions could spark fresh unrest in the nation, which is reeling from a string of killings of secular bloggers as well as the murders of two foreigners in recent months.
Earlier, the prison authorities had called the close relatives of the two convicts to see them for the last time.
With Mujahid and Chowdhury's execution, Bangladesh has hanged four war crimes convicts so far.
Two other 1971 war crime convicts Abdul Quader Mollah and Mohammad Kamaruzzaman had been executed so far.