Africa Center for Open Governance Executive Director Gladwell Otieno said Friday a panel at the High Court in Nairobi was appointed to consider her petition to halt the vote count.
"We are raising concerns about the validity of the entire process," Otieno told The Daily Nation newspaper in Kenya.
The petition was filed against the Independent Electoral Boundaries Commission and its chairman, Isaack Hassan. Hassan early this week said there were complications with the voting, which took place under new laws meant to avoid a repeat of a bloody 2007 election aftermath.
Current votes totals indicated Kenyan Deputy Prime Minister Uhuru Kenyatta has about 4.7 million votes and Prime Minister Raila Odinga has about 4.1 million, the Kenyan newspaper reports. A runoff will be called if neither candidate can get a simple majority.
Political conflict that erupted following Odinga's election objections in 2007 led to charges filed by the International Criminal Court against top Kenyan leaders, including Kenyatta. The ICC on Thursday set a provisional trial date for July 9.
Kenyatta was cleared to run in this year's presidential election in Kenya by a national court that said he was innocent until proven guilty.