Mr Najib said such protests were "not the proper channel to voice opinions in a democratic country".
He has denied pocketing $700m (£455m) of public money.
The payments, first revealed by the Wall Street Journal, came from the 1MDB state investment fund, which Mr Najib set up on coming into office in 2009.
Mr Najib has removed several leading officials who had criticised his handling of the scandal.
Malaysia's anti-corruption agency has effectively cleared him, saying the money was from foreign donors.
Protests show 'immaturity'
Police says about 25,000 people took part in the two-day demonstration at their peak, though Bersih [Clean] - the pro-democracy group behind the rallies - put the figure at 300,000.
Speaking in a public address to mark Malaysia's National Day, Mr Najib said it was clear the rest of Malaysia backed the government.
"We will never allow anyone from within or from outside, [to] simply walk in and steal, ruin or destroy all that we have built so far," the state news agency Bernama quoted him as saying.
"Let us all remember, if we are not united, lose our solidarity and cohesion, all problems will not be resolved, and everything we have laboriously built will be destroyed just like that."
He said protests which "disrupt public order and only inconvenience the people" did not reflect maturity and were "not the proper channel to voice opinions in a democratic country".
What is 1MDB?
• The 1Malaysia Development Berhad (1MDB) state investment fund was established under Prime Minister Najib Razak when he took office in 2009 to transform Malaysia into a high-income economy.
• Critics say the fund overpaid for many of its investments and spent millions on fees to investment bank Goldman Sachs
• It began attracting attention at the end of 2014 when it started missing payments to creditors. It later emerged that the fund was mired in $11bn (£7bn) of debt.
• Mr Najib has been accused of taking $700m from the fund - a charge which he has denied.
• Malaysia anti-corruption commission said it had verified that the money was a donation from unnamed foreign donors.
Mr Najib's coalition, Barisan Nasional, has governed Malaysia since independence 58 years ago.
But its support has declined in recent elections, and its critics have accused it of arrogance.
The movement against Mr Najib has been driven by influential former Prime Minister Mahathir Mohamed who was also at the rally in Kuala Lumpur on Sunday.
Mr Mahathir, who led Malaysia from 1981-2003 and was formerly a Najib ally, said it was untenable for him to continue in his position.
"There's no more rule of law. The only way for the people to get back to the old system is for them to remove this prime minister," he said. "We must remove this prime minister."
The rally in Kuala Lumpur was deemed illegal, but was allowed to go ahead, and ended peacefully late on Sunday.
Previous rallies held by the Bersih movement have been dispersed by police using tear gas and water cannon.