Thousands of protesters marched on Saturday to a police office in the north of Myanmar's largest city Yangon, demanding speedy and transparent justice in a child-rape case that has sparked national outrage.

Police said this week they had arrested a suspect in the rape of a toddler nicknamed Victoria in May, at a private nursery school in Naypyitaw, the administrative capital.

Social media users have criticized the speed and professionalism of the police response after the girl's family filed a complaint more than a month ago.

Organizers estimated as many as 6,000 protesters gathered on Saturday at the Yangon office of the Criminal Investigation Department (CID) wearing white T-shirts, some printed with the words "Justice for Victoria." One banner read: "We don't want any more Victorias."

"We need an explanation that people can accept and justice for the kid," said 33-year-old protest organizer Aung Htike Min.

The protesters also called on the government to create a safe environment for Myanmar's children.

The police force's deputy director general, Aung Naing Thu, said police had filed a case at court against a driver at the victim's nursery during a news conference broadcast live on Facebook on Friday and that the driver is in custody.

A thorough investigation was conducted, he added, but efforts to identify the perpetrator had been delayed because officers were waiting to speak to the victim, a three-year-old girl who was recovering from the medication given after the assault.

"We filed the lawsuit against the suspect based on the testimony of the child and technical records," said Aung Naing Thu, referring to security camera footage that he said implicated the driver. 

The nursery had also been closed because it lacked the correct license to operate, he added.