HONG KONG, Sept 29 (Reuters) - The Hong Kong Monetary Authority sold HK$1.039 billion ($134.1 million) into the market in New York trading hours after the currency hit the strong end of its trading band, according to data released by the HKMA.

The aggregate balance - the key gauge of cash in the banking system - will increase to HK$243.528 billion ($31.42 billion) on Sept. 30, an HKMA spokesman said early on Tuesday.

The Hong Kong dollar is pegged in a narrow range of 7.75-7.85 to the U.S. dollar. The HKMA has been conducting sales in recent sessions to weaken the currency to keep it within that trading band. ($1 = 7.7496 Hong Kong dollars) (Reporting by Donny Kwok; Editing by Jacqueline Wong)