The three are leaders of the four parties in Mahathir's alliance, which scored a stunning election victory Wednesday by ousting the coalition that had ruled Malaysia since independence from Britain in 1957.
"His initial focus will be mostly domestic issues - executing campaign promises and reducing inefficiencies so that the government can still maintain fiscal discipline", said Hasan Jafri, who heads Singapore-based business consultancy HJ Advisory.
He gave no reasons for the authorities' decision, but said he would abide by it.
"We accept the people's verdict with an open heart".
Najib had faced accusations of corruption and mismanagement over the state investment fund 1Malaysia Development Berhad (1MDB).
Also Saturday, Mahathir appointed Lim Guan Eng, an ethnic Chinese, as finance minister, the first ethnic minority to be appointed to the powerful post in 44 years.
Already, rifts are beginning to show. Mr Mahathir sacked Mr Anwar from his post as deputy prime minister and jailed him on a dubious sodomy charge in 1999.
Cukup Pendapatan Mansuhkan GST (Enough Funds To Abolish The GST) - Berita Harian reported that the Prime Minister vehemently emphasised that the country's income will not decrease in the absence of the GST as he blamed misused funds and wastefulness as the root cause of the decrease.
"Leave it to us", he said when asked how the tycoon would be brought back to Malaysia to answer for the 1MDB scandal. This will necessarily mean that while Malaysia can, should and likely will further develop a policy of "trade with all", it can also work to decrease geopolitical tensions with conflicting superpowers, especially regarding United States antagonism of China in the South China Sea and in ASEAN more widely.
Far from just being an ideal situation, this is the new reality of Malaysian politics where an old experienced leader has teamed up with a multipolar minded and multiracial minded party to help form the core of a new political programme for all Malaysians.
Lim's main priority will be to reassure investors he can carry through Mahathir's populist spending pledges without increasing government debt.
Financial markets had been betting on Najib remaining in power, and the currency and stocks are set for more volatility when markets reopen on Monday.
Malaysia is among the first few countries to introduce a law against it. Germany approved a plan previous year to fine social media networks if they fail to remove hateful postings. The central bank under her had urged criminal proceedings at least twice against the troubled state fund, before slapping a fine of an undisclosed amount on 1MDB, days before she left the position.
Daim Zainuddin is also a member of the council, and served twice as finance minister under Mahathir, helping spearhead Malaysia's economic recovery after the Asian crisis.
Daim spends part of his time in Africa "engaging African governments on economy and planning", according to his web site.
Shares in AirAsia Group Bhd fell as much as 10 percent after its chief Tony Fernandes apologized for endorsing former prime minister Najib Razak in the election.
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