The airport (KLIA2), purpose built for budget airlines, handled more than 3 million passengers during its first month in May and Mr Najib said he expected it to serve 25 million passengers by the end of this year, The Star reported on Wednesday.
It can handle 45 million passengers a year and will serve Malaysia for up to 15 years, he said.
The airport would play a key role in making Malaysia an aviation centre in the region, he added.
The new airport was built adjacent the original Kuala Lumpur International Airport in Sepang. The two airports serve its capital.
Malaysia has set aside 700 million ringgit (7 billion baht) to upgrade KLIA so it can handle more air traffic and another 300 million ringgit to improve other airports in the country, according to the Malaysian prime minister.