Tower Hamlets LBC is also set to receive government cash in the wake of last February's IRA bomb attack on Canary Wharf.
But Manchester expressed concern that the DoE is only prepared to award assistance for costs incurred within two months of the attack.
Manchester finance chair Cath Inchbold said: 'We are glad the government has responded but we are worried they suggest a two-month time limit following the event for calculating how much help we may receive.
But Ms Inchbold welcomed the fact that ministers would take into account income lost to the council from car parking and trading at the Arndale Market.
Manchester has submitted a£5.1 million bill to the DoE. Any assistance given will be via a special grant awarded under the Local Government Act 1988 rather than the Bellwin scheme.