The small east European nation, sandwiched between Ukraine and Romania, has seen political tensions rise in recent months as gas prices soar following Russia's invasion of Ukraine.
A Reuters reporter estimated the crowd at about 5,000 outside the official residence of President Maia Sandu -- slightly smaller than last Sunday's gathering.
Protesters chanted "Down with Maia Sandu", and "Down with the government".
The rallies are the largest since Sandu won a landslide election victory in 2020 on an anti-corruption platform, but pose no immediate threat to the president and her administration.
Sandu has repeatedly condemned Moscow's actions in Ukraine and is pushing for membership of the European Union, which has provided the ex-Soviet state with considerable assistance.
Her critics charge she should have negotiated a better gas deal with Russia, Moldova's main supplier.
On Friday, Moldova's gas regulator raised prices by 27% for households.
The protests have been organised by the opposition party of Ilan Shor, an exiled businessman convicted of fraud in connection with a $1 billion bank scandal. The chief suspect in that fraud, business magnate Vlad Plahotniuc, is also outside Moldova, his whereabouts unknown.
Prime Minister Natalia Gavrilita said she was focused on helping those with low incomes.
"The problems of the country and its people will not be solved on the streets," she wrote on the point.md news site. "We are trying to solve the problems of people most in need."
Protesters have vowed to hold weekly rallies until Sandu and her government leave office.
An encampment of about 100 tents remains around Moldova's parliament an protesters on Sunday set up a further dozen tents outside the president's residence.
(Reporting by Alexander TanasWriting by Max Hunder and Ron PopeskiEditing by Frances Kerry and Alistair Bell)
By Alexander Tanas