Derek McCallan told BBC NI's The View programme that political uncertainty was not good for local government.
Last month, Stormont's power-sharing institutions collapsed over the fall-out from a botched green energy scheme.
A snap election will now take place on 2 March.
Mr McCallan said that the sooner "normal service is resumed", the better from the perspective of NILGA.
However, he added that if it is not resumed, a devolution bill "that goes beyond Stormont" is needed.
"Eleven councils now, seamlessly since 1972, have been delivering services, and they want to plan their local economies," he said.
"They want to assemble land, they want to get regeneration, they want to work with other government departments.
"If there isn't a budget in this looming uncertainty, then give the councils the power and the resources to do the job."
Last week, the head of Bombardier in Northern Ireland, Michael Ryan, said the manufacturing sector also needs to see a swift political resolution at Stormont.
Mr Ryan was speaking at an event that highlighted the importance of having an industrial strategy in Northern Ireland.
The head of the Northern Ireland Local Government Association (NILGA) has said councils should be given more powers if the Stormont Executive faces a long period of inaction.