An LAPD spokeswoman said "a lot" of phone tips were coming in, but none had led police detectives to the abducted children.
"We've been getting a lot of vehicle calls," said Sgt. Shannon Paulson of the Los Angeles Police Department Hollenbeck Station. "We prefer more calls and we're making every effort to follow up on everything that comes in."
The children were last seen at their grandmother's house on the 1400 block of Indiana Street in Boyle Heights Friday.
Police say the kids were forcibly taken by their biological parents, Enrique Felix and Rose Chairez, both 28. The couple does not have custody of the children due to abuse allegations.
The children - 7-year-old Enrique Junior, 5-year-old Justin and 1-year-old twins Veronica and Janet - were under the care of their maternal grandmother.
Police said the parents were only allowed to see the children during supervised visits at the Los Angeles County Department of Children and Family Services.
Police believe the kids could be in danger. Felix was physically violent toward them and their mother in the past, police said.
Felix is 5 feet 10 inches tall, 200 pounds with black hair and brown eyes. Chairez is 5 feet 3 inches tall, 150 pounds with red hair and brown eyes.
The parents' car was described as a gray PT Cruiser with tinted windows and no license plate. The car has paper plates with some type of black lettering on it and a missing right-rear hubcap. The LAPD says the suspects may also have access to a green Ford Expedition with the California license plate 4LPF643.
Madera encouraged the public to contact police with any tips.
Anyone with information regarding the case or the whereabouts of the four children, as well as Felix and Chairez, was asked to call Los Angeles police at (323) 342-4100.
CNS contributed to this report.