Nairobi, Kenya (CNN) -- Three Kenyan political leaders accused of crimes against humanity following the country's disputed 2007 elections had their first appearance Thursday before the International Criminal Court at The Hague.

Another three are scheduled to appear Friday.

The court's top prosecutor, Luis Moreno Ocampo, named the six as suspects in December, claiming they organized violence that left more than 1,000 people dead and displaced hundreds of thousands more.

Former Agriculture Minister William Ruto, opposition leader Henry Kosgey and radio journalist Joshua Arap Sang appeared Thursday. Deputy Prime Minister Uhuru Kenyatta, Cabinet Secretary Francis Muthaura, and former national police chief Hussein Ali are set to appear Friday.

The two groups of three come from opposite sides of the political dispute in Kenya.

Ruto, Kosgey, and Sang face four counts of crimes against humanity: murder; deportation or forcible transfer of the population; torture and persecution.

The judge set a date for them of September 1 to hear arguments as to whether they should go to trial.

Judge Ekaterina Trendafilova quashed their attempts to plead their cases Thursday.

When asked whether he understood the allegations, Ruto said he did, but that "the allegations sound like they came from a movie."

Trendafilova warned the suspects that they should refrain from political activities relating to the case.

"It has come to our knowledge," she said, "that there are some movements towards triggering the violence in the country by way of some speeches. Such type of action could be seen as an inducement and could constitute a breach of conditions."

She warned that if the suspects continued in such a vein that the summons could be turned into "warrants of arrest."

By late April, the two sides need to meet to start sharing evidence, the judge said.

Last month, Kenya challenged the jurisdiction of the International Criminal Court, saying its own authorities will investigate and prosecute the cases on Kenyan soil. The Netherlands-based court calls itself, on its website, "an independent international organization ... established to help end impunity for the perpetrators of the most serious crimes of concern to the international community."

Kenya's disputed presidential election sparked chaos that escalated into ethnic violence pitting supporters of incumbent President Mwai Kibaki against those of challenger Raila Odinga, who was later named prime minister in a power-sharing agreement.

Muthaura, Kenyatta and Ali are accused of committing or contributing to the killing, rape and other acts of violence against supporters of the opposition Orange Democratic Movement.

Ruto, Sang and Kosgey are accused of being co-perpetrators in the murder, deportation and commission of other offenses against supporters of Kenya's Party of National Unity.

E.J. Hogendoorn of the International Crisis Group said the case is "a major victory, especially for civil society in Kenya, and it is potentially a significant step to the end of impunity in Kenya."