NatWest, owned by the Royal Bank of Scotland, has now lost its bid to have the relatives' compensation claim thrown out of the US court.
The suit was filed in a US federal court in January by 15 families related to the 20 victims of a bus bomb planted by Hamas in 2003.
NatWest had supported UK charity Interpal, the relatives argued, which the US government has named as a specially-designated global terrorist organization in August 2003 and was believed to be behind the bombings.
But NatWest insist that the British Charity Commission had proved Interpal innocent before any case was filed.
But this argument has not convinced US District Judge Charles Sifton who says the bank's defense is not strong enough.
"Because each attack was preceded by at least one relevant transaction by NatWest, plaintiffs have sufficiently alleged that each attack was proximately caused by NatWest," Reuters reports the judge as saying.