"Moldova does not want to be blackmailed by the Kremlin," Sandu said at the rally, which was organised by her government and packed a central square.
Police said more than 75,000 demonstrators were present.
"We don't want to be on the outskirts of Europe anymore," she said, pledging that Moldova would become an EU member by 2030.
European Parliament President Roberta Metsola, on a visit to Chisinau, also addressed the rally, saying Europe would welcome Moldova "with open arms and open hearts".
"This is about the both of us: You will bring a piece of Moldova to Europe, and you will make Europe stronger," she said.
Demonstrators called on Moldova's political leaders to amend the constitution to specifically mention the country's European orientation.
"I believe in a European Moldova and want for my country a future with advanced economic and socio-political development," said 18-year-old attendee Alexandrina Miron.
"Right now we are a little behind, but we will slowly catch up and stand on par with Europe."
The leader of the pro-Russian opposition Shor party, exiled businessman Ilan Shor, told his supporters at rival protests in several cities via video link that he would seek a referendum on Moldova's foreign policy.
Shor, sanctioned by the U.S. as an agent of Russian influence in Moldova, was handed a 15-year jail sentence in absentia last month for his role in the 2014 theft of $1 billion from Moldovan banks.
