Three militants, including Mufti Abdul Hannan, the head of the Harkat-ul Jihad Islami group, were convicted and sentenced to death in 2008. Three people were killed in the May 21, 2004, attack and about 50 wounded, including then British High Commissioner Anwar Choudhury, who was hit in the leg.
Suicide attacker targets Bangladesh army camp
A panel of three judges headed by Chief Justice Surendra Kumar Sinha rejected the petition that sought a review of the death sentences, Attorney General Mahbubey Alam said.
"Now there is no legal bar to hang them, unless they seek clemency from the president and the president pardons them," Alam told reporters.
Defense lawyer Nikhil Kumar Saha said: "It is up to them whether they will seek clemency from the president or not."
The Supreme court upheld their death sentences last year.
Bangladesh police kill militant
Harkat-ul Jihad Islami was blamed for several other attacks, including a bomb blast later in 2004 at a rally by then opposition leader Sheikh Hasina, who later became prime minister. That attack killed 23 people and wounded more than 150. Hasina suffered partial hearing loss.
Hannan was also sentenced to death for a bomb attack on a Bengali New Year's celebration in 2001 that killed 10 people dead and wounded scores.
Sunday's ruling came amid rising concern over the growth of Islamist militancy in the Muslim-majority South Asian country of 160 million people.
There has seen a series of deadly attacks in recent years, the most serious last July when gunmen stormed a Dhaka cafe and killed 22 people, most of them foreigners.
Police have killed more than 50 militants since the cafe attack.
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