Former Malaysian prime minister Dr Mahatir Muhammad. PHOTO: AFP
Mahathir, 90, who was Malaysia's longest-serving prime minister, electrified crowds at the demonstration in Kuala Lumpur on Sunday by calling for a sustained public push to topple Najib.
He also accused Najib of bribing politicians in the ruling party, the United Malays National Organisation (UMNO), to secure their support and said the premier was clinging to power to avoid corruption charges.
"We will call him (Mahathir). He has made speeches and accusations," national police chief Khalid Abu Bakar was quoted as saying by online news outlet Malaysiakini.
"Among them, he claimed UMNO leaders had taken bribes so we want to find out more."
The report gave no further details.
The ruling coalition led by UMNO routinely hauls in opponents who take part in anti-government actions, in what the opposition calls a pattern of systematic harassment.
Mahathir himself took a hard line on dissent during his 1981-2003 term of office.
It was not clear whether Mahathir, who remains influential in the ruling party, would face any charges.
Seven people from Bersih, the coalition of Malaysian NGOs and activist groups that staged the weekend demonstrations, were questioned by police on Wednesday. No charges were filed.
A lawyer representing Bersih, Ramkarpal Singh, said police were investigating the organisers over various assembly violations.
"They should not be prosecuted or persecuted for holding a peaceful rally," he said.
Najib has been under growing pressure since The Wall Street Journal revealed in early July that Malaysian investigators had found nearly $700 million in mysterious deposits into his personal bank accounts.
His government has since admitted the deposits were made, calling them "political donations" from Middle Eastern sources but refusing to give further details.
Outrage over the scandal has been heightened by subsequent government personnel moves by Najib — including sacking Malaysia's attorney general — that appear to have stalled investigations.
Najib had already been facing demands for months that he explain the whereabouts of huge sums allegedly missing from deals involving a state-owned company he launched.
He denies any wrongdoing, saying he is the victim of a "political conspiracy".
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