Speaking at a conference in Kuala Lumpur, Mahathir, referring to Beijing, said Lam 'has to obey the masters and at the same time she has to ask her conscience.'
The region's online industry has more than tripled in the past four years alone as young users turn to their phones to do everything from banking, playing games and purchasing plane tickets.
The law gives government ministers powers to order social media sites to put warnings next to posts authorities deem to be false.
The biggest march remained on Hong Kong island, a frequent battlefield between police and protesters.
The fire has now been largely put out.
More than 100 people were also injured and at least 15,000 people had to evacuate because their houses were damaged by the strong jolt.
October 1 is "U-Day", when Myanmar officially adopts the new system.
On Wednesday, the Search and Rescue Agency said that four bodies were discovered near the wreckage of the small plane.
Mahathir said the government will first wait for the results of the police investigation into the alleged inflammatory remarks made by him against minorities in Malaysia, reported Malay Mail.
Rakhine state is one of Myanmar's poorest regions and NGOs provide aid to tens of thousands of Rohingya Muslims still languishing in displacement camps as well as other local communities.
Myanmar has repeatedly said it is ready to take back refugees, blaming Bangladesh for failed efforts to kick-start returns.
UN special rapporteur Yanghee Lee called for the commanders' assets to be frozen.
Travel ban on Myanmar military leaders not enough: UN investigator calls for commanders' assets to be…
Each year thousands of Rohingya and stateless Bangladeshis try to reach Malaysia or Indonesia by sea.
The Myanmar proposal to list the site was approved at a meeting of the UN's cultural body in Baku, Azerbaijan.
A 2017 military crackdown drove more than 730,000 Rohingya Muslims to flee to Bangladesh.