Motiur Rahman Nizami, 72, was seeking a review of the Supreme Court decision to uphold a war crimes tribunal verdict.
He was convicted of genocide, rape and torture, charges the defence said were not proven beyond reasonable doubt.
Unless he seeks clemency from the president he could be hanged in days.
His party responded to the Supreme Court decision by calling a nationwide strike for Sunday and has said it will hold street protests. Security has been tightened across the country.
"All the legal battles are over," a lawyer for Nizami told reporters. "Now it is up to him, whether he will seek clemency from the president, or not."
Correspondents say it is unlikely clemency would be granted, even were Nizami to appeal.
Four politicians have so far been hanged for war crimes since the controversial tribunal was set up in 2010. Scores of people have been killed in violence following previous judgements.
Bangladesh Islamist leader Motiur Rahman Nizami loses final appeal
05 May 2016
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The head of Bangladesh`s largest Islamist party has lost a final appeal against his death sentence for atrocities committed during the war of independence from Pakistan in 1971.
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