Malaysia's new prime minister Anwar Ibrahim vows to unify the country and fight corruption

New prime minister Anwar Ibrahim has pledged to make "Malaysia for all Malaysians," fight corruption and reiterated that he won't be taking a salary as Malaysians battle rising costs of living. 

Anwar, who has campaigned for 24 years for the top job in Malaysia amid political coups and jail sentences, said improving the Southeast Asian nation's economy will be his priority. He added that China remains pivotal to Malaysia's economic interests. 

Fielding questions at a full-house press conference after being sworn in as the country's 10th prime minister on Thursday, Anwar said he would push to make Malaysia a place that does not marginalize or neglect any groups, including the eastern states of Sabah and Sarawak. 

"[Earlier] my grandson asked me how long have you got to wait [for the swearing-in ceremony]? I said not long, only 24 years," he said at the Sungai Long Golf and Country Club in Kuala Lumpur. 

He said that despite "trials and tribulations," and even though others tried to "scuttle and frustrate" his pathway to the premiership, "I am proud to say that we did achieve — not for Anwar, not for the ministers, not [for] the party leaders but to give the new sense of confidence to all Malaysians. It is their land, and it is their country."

"There are some core issues that we will never compromise [on]," he said, citing good governance, anti-corruption issues and judicial independence.

"And, more importantly, the issue of the welfare of the ordinary 'rakyat' which includes the issue of cost of living," he said, using the Malay word for citizens.

Congratulations poured in from leaders from all over the world including Indonesian President Joko Widodo and Singapore Prime Minister Lee Hsien Loong. 

As journalists waited for the press conference to start, Anwar took a phone call from Turkey President Recep Tayyip Erdogan, who he said had "waited two hours" to speak to him. 

The two leaders had an audible conversation about deepening bilateral relations. 

Anwar's long-time rival Mahathir Mohamad also congratulated him on social media. In a change of tides, the former strongman, who led Malaysia for decades, lost his parliamentary seat in the latest election. 

Anwar was deputy to Mahathir in the 1990s but their relationship ran afoul and Anwar was sacked and eventually charged with sodomy.

When asked about China during the press conference, Anwar said that he would build on the relationship with China just like he would with other countries. 

"China is an important neighbor. It is a priority to enhance bilateral relations with China, trade, investments. I will not just leave it as this, I think it needs to be enhanced. Similarly, we need to relate to the United States, with Europe … with ASEAN," he said, referring to the 10-nation Southeast Asian bloc.

Before he can execute new policies, Anwar faces another test next month after saying he would table a motion to hold a confidence vote on the first day of parliament on Dec. 19. 

The risky move comes as his rival Muhyiddin Yassin, and leader of competing coalition Perikatan Nasional, continues to challenge him on proof that he had majority support. 

Perikatan Nasional won 73 seats and was runner-up to Anwar's Pakatan Harapan which won 82 seats.

Anwar confirmed during the press conference that in addition to the seats his coalition won, he also received support from Barisan Nasional which won 30 seats and Gabungan Parti Sarawak which won 23 seats. That takes him past the 112-seat simple majority needed to form a government. 

The election on Saturday produced a hung parliament for the first time in Malaysia's history.

ISEAS Yusof Ishak Institute senior fellow, Francis Hutchinson told CNBC's "Squawk Box Asia" on Friday that on top of having the difficult task of stabilizing the economy and securing a cabinet, Anwar will have to find a way to win over voters who did not directly vote for his coalition Pakatan Harapan. 

"There are many people who voted for Perikatan Nasional, Bersatu and PAS that would be feeling disenfranchised and left out," Hutchinson said. 

"So I think that there does need to be some sort of effort to go across and establish why these people voted the way they did, and where there is common ground."

When asked if Anwar had cut a deal with Barisan Nasional to pardon jailed former prime minister Najib Razal in return for getting their support, Hutchinson said: "We can kind of put Najib to one side for the moment" as his conviction was a result of a very comprehensive legal process. 

Najib was sentenced to 12 years in jail, after being charged for his role in the embezzlement of billions of dollars from 1Malaysia Development Berhad (1MDB).