Initially peaceful rallies that started last month against planned tax rises descended into violence with dozens killed after some marchers stormed parliament.
Ruto shelved his tax reform and proposed a national dialogue.
"Justice must come first before any talks," said Odinga on Sunday, however.
He also demanded "compensation for every victim of police brutality" during the rallies.
Despite Ruto's concessions, rallies have continued across the country. The opposition has called for fresh demonstrations next week.
"I want to promise it is going to stop. Enough is enough," Ruto said on Sunday.
A court on Thursday suspended a police move to ban protests in the center of the capital Nairobi. Ruto vowed to stop "looters" and "killers" who he said "risk destroying our country".
"We want a peaceful, stable nation. And our issues are resolved using democratic means," he said.
Odinga, 79, who lost out to Ruto in the 2022 presidential election, said there had to be a "national conversation" between different sectors of society. Such discussions, he said in a post on X, "should come from various sectors including youth, government, religious leaders, health care professionals, lawyers and teachers".
Ruto on Friday unveiled a new partial cabinet to lead a "broad-based" government in a bid to ease the worst crisis of his nearly two years in office. But the main opposition coalition swiftly branded the cabinet moves "cosmetic" and insisted it would not join a government of national unity led by Ruto.