KUALA LUMPUR—Malaysia’s government is pushing ahead with its promise to abolish the death penalty, a move that sits at odds with the use of capital punishment elsewhere in Asia.

Liew Vui Keong, minister in the prime minister’s office, said Thursday that the paperwork to abolish the death penalty in Malaysia is now in its final stages after the cabinet approved the measure on Wednesday. The proposal could be presented to Parliament when the next session begins on Oct. 15.

The...