NAIROBI, Kenya — Kenya’s deputy president, William Ruto, rose before the International Criminal Court for the start of his trial on Tuesday and three times — once for each charge of crimes against humanity facing him — repeated the words “Not guilty.”

With Mr. Ruto’s appearance before the court in The Hague for his role in the violence that rocked the country after the disputed 2007 election, a process began that could influence not only the future of Kenya but also of the much-criticized tribunal as well.

The scrutiny will continue to intensify, particularly once the Kenyan president, Uhuru Kenyatta, joins Mr. Ruto in facing charges before the court in November. It will be the first time a sitting president has appeared before the court to stand trial.

The case represents a pivotal moment for the court, and one that is not without risks. The tribunal finds itself the object of significant ire in Kenya and elsewhere on the continent because all eight of the cases on its docket are from Africa. Earlier this year, the African Union accused the court of targeting Africans.