The leaders said they would not carry out the ritual that is normally performed for every Muslim, regardless of their actions.
In a statement on social media, the group said: "Consequently, and in light of other such ethical principles which are quintessential to Islam, we will not perform the traditional Islamic funeral prayer over the perpetrators and we also urge fellow imams and religious authorities to withdraw such a privilege.
The statement added: "This is because such indefensible actions are completely at odds with the lofty teachings of Islam."
Religious leaders of all backgrounds have condemned the attack which killed seven and injured 47 on Saturday evening when three men rammed a rental van into pedestrians then randomly stabbed revellers in bars and restaurants near Borough Market.
A panel of speakers at the East London Mosque said they would work to combat extremists' "twisted narrative and their perversion" of religion.
"Once again we come together, to stand united against those who try to divide us," said the chairman of East London Mosque and London Muslim Centre, Muhammad Habibur-Rahman.
"The cold-blooded murder of innocent people in London on Saturday evening will not succeed in driving us apart.
"I have a clear message to those who perpetrate terrorism: you are against the very core teaching of Islam and of our Prophet Muhammad, peace be upon him.
"Your misguidance will lead you to destruction, and God willing you will utterly fail in your evil aims.
"We stand apart from you and your corruption of the religion of Islam. Terrorism has no faith."
The sentiment was echoed by Theresa May on Sunday morning, who said the terrorists were "perverting the truth" of Islam.
She declared that "enough was enough" and pledged to reform legislation around internet activity. The Prime Minister also said there should be "embarrassing conversations" about Muslim communities in the UK that have failed to integrate, but did not specify further detail, despite of many Muslim leaders condemning the attacks.
Police have named two of the attackers as Khuram Shazad Butt and Rachid Redouane.
The former was known to MI5 and police but authorities said there was no evidence he had planned an attack.
Redouane was not known to police. The third attacker has not yet been named.
A total of 12 people were arrested during a police raid in Barking, London in the hours after the attack.
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