The 51-year-old man attacked the children using knives in both hands while they were waiting to board a bus to Caritas elementary school, the police said.
An 11-year-old girl and a 39-year-old man died in the rampage, according to authorities. The suspect also died of self-inflicted injuries at a hospital, local news agency Kyodo reported.
The police named the victims of the fatal attack as Hanako Kuribayashi, who was in the sixth grade, and Foreign Ministry official Satoshi Oyama, who is believed to be the parent of another child.
The motive behind the incident, which was carried out near a park in Kawasaki's Noborito area at 7.45 a.m., was not yet known and the suspect was not named.
According to eyewitnesses, the suspect approached the children, yelling "I'm going to kill you". The police retrieved two knives at the scene and found two more in a backpack believed to be belonging to the suspect.
The driver of the Caritas bus told public broadcaster NHK that he saw a man approach the queue of students. He began stabbing the children and then boarded the bus and stabbed children inside as well.
"I heard fire engines coming in the morning and I saw a man lying on the ground bleeding," said a witness, adding that he saw many elementary schoolchildren lying on the ground near a school bus stop and school rucksacks were scattered all over the place.
Japanese Prime Minister Shinzo Abe condemned the attack, saying he felt "strong anger" against it.
"It is a very harrowing case. I offer my heartfelt condolences to the victims and hope the injured recover quickly," he said.
The incident took place during US President Donald Trump's visit to the country. Speaking aboard a Japanese helicopter carrier, he said that "all Americans stand with the people of Japan and grieve for the victims and for their families".
( With inputs from IANS )