Aug 13 (Reuters) - Insurance broker Arthur J Gallagher & Co said on Friday it had agreed to buy the treaty reinsurance brokerage business of Willis Towers Watson for an initial consideration of $3.25 billion.

The deal, which includes a potential additional consideration of $750 million, comes weeks after Willis and rival Aon Plc called off a $30 billion merger that would have created the world's largest insurance broker.

Treaty reinsurance involves reinsuring the whole of an insurer's book of business, rather than individual projects or risks. (Reporting by Noor Zainab Hussain in Bengaluru' Editing by Sriraj Kalluvila)