Victims in the case against President Uhuru Kenyatta at the International Criminal Court (ICC) want the prosecution ordered to conduct fresh investigations.
The victims also want investigations reopened against former Head of Public Service Francis Muthaura and former Police Commissioner Hussein Ali.
In an application filed at the court on Monday, the victims' lawyer Fergal Gaynor wants the Pre-Trial Chamber to review a decision by the Office of the Prosecution not to conduct further active investigations in the case.
In 2012, The Pre-Trial Chamber declined to confirm the charges against Mr Ali and a year later, the prosecution dropped the case against Mr Muthaura. Uhuru's case was dropped last year.
The lawyer claims the cases collapsed due to failure by the prosecution to carry out thorough investigations and high-level campaign by the Kenyan government against the ICC. He also accused the State of obstruction of access to evidence relevant to the cases.
"This took place simultaneously with efforts to bribe and intimidate key witnesses," Gaynor said.
The Prosecution has indicated that they have ceased active investigation after concluding that at the moment there are no prospects of strengthening their evidence without genuine cooperation from the Kenya government.
"The investigation and prosecution of all three persons were manifestly ineffective. All charges against all three collapsed, before a single day of trial. The court's credibility and deterrent effect were damaged. Instead of encouraging inter-ethnic peace and reconciliation, the collapse of all charges and the prosecution's decision not to further investigate have instead created feelings of bitterness and anger in the victims. A less effective investigation or prosecution is difficult to imagine," Gaynor said.
"The victims are asking the judges to review the legality of the prosecutor's decision to cease active investigation. They want the judges not to confirm that decision until they are satisfied that the prosecution has complied with its obligation to carry out prompt, thorough and effective investigations and prosecutions concerning the crimes committed against the victims during the 2007-2008 post election violence," the lawyer said.