Bahasa Melayu* = Primary language spoken in Malaysia, Brunei

The Kuala Lumpur City Guide says,

Bahasa Melayu is the official language of Malaysia and Brunei. Together with Bahasa Indonesia (Indonesian form of Malay), the language is spoken by around 200 million people, making it world's 8th most widely spoken language.

The forms of Malay vary slightly in different countries - but is exactly the same in Malaysia and Singapore. The vocabulary of the language is enriched by influence from Sanskrit (ancient Hindi), Arabic and since 19th century, English. Kuala Lumpur City Guide

The Portuguese word for "Malayu" is "Malaio."