One week after the shock resignation of Mahathir Mohamad as Malaysia's prime minister, the country now has a new premier — but some analysts said the political crisis is not over yet. Muhyiddin Yassin, former minister of home affairs under Mahathir, was sworn in as Malaysia's 8th prime minister on Sunday after emerging as a frontrunner for the top job at the end of last week. But Mahathir has claimed that he, instead of Muhyiddin, has the support of the majority in the country's 222-seat parliament. The FTSE Bursa Malaysia KLCI Index fell by more than 1% on Monday morning before recouping some losses to trade about 0.3% lower. In contrast, many of its regional peers gained. "We consider Malaysia's political crisis far from over as we are dealing with yet another fragile coalition here. And this is not positive for investors and markets," Prakash Sakpal, Asia economist at Dutch bank ING, wrote in a note. The Malaysian government has for decades been made up of a coalition of political parties. Muhyiddin's party, Parti Pribumi Bersatu Malaysia or Bersatu, was part of the former ruling coalition called Pakatan Harapan. Muhyiddin pulled his party out of the coalition last week after Mahathir's resignation, which resulted in the collapse of the previous government. He subsequently tied up with several parties, including the United Malaysia National Organisation or UMNO, which lost power in the 2018 general elections.

The opportunists who don't want to miss out on cabinet posts might now be tempted to jump ship... Harrison Cheng Control Risks

Muhyiddin was believed to have 113 members of parliament on his side, according to various local media reports, citing unnamed sources. That's more than the 112 lawmakers needed to form a government in Malaysia. But ahead of the swearing-in ceremony, Mahathir — who set up Bersatu with Muhyiddin — said 113 members of parliament had pledged their support for him to return as premier. Some of those on Mahathir's list have denied supporting the former premier. But if the numbers hold, analysts said Mahathir could file a no-confidence motion during the next expected sitting of parliament next Monday, on March 9. "Whether Muhyiddin will face a no-confidence motion really hinges on whether the 113 MPs pledging support for Mahathir continue to stick together by then," said Harrison Cheng, associate director and lead analyst for Malaysia at consultancy Control Risks.

"The opportunists who don't want to miss out on cabinet posts might now be tempted to jump ship, though Mahathir's published list of MPs could have drawn the lines such that it now makes no sense to move over, given that they have been explicitly identified as Mahathir supporters," Cheng wrote in a note. But Adib Zalkapli, a director at consultancy BowerGroupAsia's Malaysia office, said it's unlikely the speaker of parliament would allow lawmakers to vote on a no-confidence motion. "Parliament is convened primarily to transact government's business and the government decides the agenda of parliament, so it's unlikely for (Muhyiddin's) appointment to be challenged," he told CNBC's "Squawk Box Asia" on Monday. Instead, the closest to a no-confidence motion that the Malaysian parliament has seen is the budget bill that the government typically tables at the end of the year, he added. If that bill is not passed, the government could collapse, said Adib.

Return of scandal-tarnished parties

Even if Muhyiddin could hold his numbers together, it's uncertain that the new coalition government would have a smooth ride. The prime minister's own party, Bersatu, remains divided with some members publicly pledging their support for Mahathir instead. One coalition partner, the Islamist party PAS, could attempt to push for "religiously inspired policies" that would cause friction with other allies which are moderates, said Cheng. In addition, the comeback of political parties tarnished with corruption scandals would impede reforms that the previous government had started, and anger the Malaysian public — who voted those parties out in the last elections.