Suu Kyi's National League for Democracy (NLD) party called the violence by security forces in Mandalay a crime against humanity.
Authorities have warned protesters against holding further rallies, saying that by planning a big demonstration on Monday, they were inciting anarchy and pushing young people towards a path of confrontation "where they will suffer the loss of life."
The warning failed to deter protesters, who vowed to continue to demand the restoration of democracy.
"The number of people will increase. ... We won't stop," protester Yin Nyein Hmway said in Yangon.
An increasing number of young people are participating in pro-democracy protests in Myanmar.
"As young people have our dreams, but this military coup has created so many obstacles," said Ko Pay in Yangon.
"That's why we come out to the front of the protests."
The US Secretary of State Antony Blinken said the US stands with "the people of Burma as they demand the restoration of their democratically elected government."
He also said the US would take "firm action" against Myanmar authorities' violent crackdown on those opposing the military coup, in a tweet.
Global leaders urge dialogue
On Sunday, Germany's Foreign Ministry repeated its demands "to end violence against demonstrators and instead to open up dialogue." The ministry also called for the immediate release of Suu Kyi and President Win Myint.
EU foreign affairs chief Josep Borrell slammed the use of force by the military and security forces and called on them to immediately stop violence against civilians.
The bloc's Foreign Affairs Council is to discuss the latest events in Myanmar on Monday and "take appropriate decisions," Borrell said.
State Department spokesman Ned Price said the United States was "deeply concerned" by the violence. UN Secretary-General Antonio Guterres said the lethal force was unacceptable.
In a statement released on Sunday, Myanmar's Foreign Ministry reiterated the junta's stance that the takeover was constitutional.
The ministry lashed out at some embassies and foreign governments, calling their statements "tantamount to flagrant interference in internal affairs of Myanmar."
The Foreign Ministry claimed that, despite "unlawful demonstrations, incitements of unrest and violence, the authorities concerned are exercising utmost restraint through minimum use of force to address the disturbances," adding that officers were maintaining public safety in line with domestic laws and international practices.