KUALA LUMPUR — Malaysian Prime Minister Najib Razak faces a test of his popularity this week in two by-elections that come hard on the heels of calls by the country’s former leader, Dr Mahathir Mohamad, for him to step down.

Dr Mahathir has said the ruling United Malays National Organisation (UMNO) risks losing the next election, due by 2018, if Mr Najib remains its leader. A poor showing in this week’s by-elections could weaken the premier’s position.

The ruling Barisan Nasional (BN) is widely expected to win today’s by-election for its traditional stronghold of Rompin. BN’s candidate, Mr Hasan Arifin, is running against opposition Pakatan Rakyat’s (PR) candidate, Mr Nazri Ahmad. Anything short of a resounding BN victory would be seen as a reflection on Mr Najib’s leadership, political analysts said.

“The results would be used to test whether Najib is a poison pill or a magic wand for his party,” said Dr Oh Ei Sun of the S. Rajaratnam School of International Studies in Singapore. “If the win margin diminishes compared with previous years, then one can argue that Najib’s leadership is dented.”