A motion by Chepalungu MP Isaac Ruto seeking to push the government to withdraw from the Rome Statute met stiff opposition on the floor of the house with questions of procedure and legality arising.
Those opposed to the motion argued that due procedure was not followed while bring the motion to the house and it was also unconstitutional.
Quoting article 2 of the constitution, the legislators led by Justice Minister Mutula kilonzo said the law should be followed in withdrawing from the Rome Statute.
He warned MPs against acting out of emotions following the naming of six individuals suspected to be the masterminds of the post election violence.
However, those in favour of the motion argued that parliament was supreme and it would make and amend laws when it deems right.
They further argued that it was time Kenya withdrew from the Rome Statute claiming the International Criminal Court is partial.
Deputy Speaker Farah Maalim deferred the motion and is expected to give a ruling on the issues raised.
Meanwhile, the National Council of Churches of Kenya wants the government to move with speed and establish a competent Local tribunal to prosecute all the perpetrators of post election violence.
NCCK says there are more suspects other than the six named by ICC prosecutor Luis Moreno Ocampo and it will be wise for them to face justice.
In a press conference held in Nairobi Thursday, NCCK Secretary General Canon Peter Karanja warned that failure by the government to put in place a local mechanism to deliver justice for the victims of violence will demonstrate lack of Political will to end impunity.
Karanja said ICC is doing its part and it is up to the Kenyan leaders to ensure that the rule of law prevails at all times.
He called on the political class to respect the spirit of the new constitution following the latest developments.
At the same time, NCCK wants the Waki commission report on the chaos made public to end suspicion and speculations on its content.
Elsewhere, the Kenya National Commission on human Rights has called on public servants on the International Criminal Court list of suspected masterminds of the post poll chaos to resign.
Addressing the press, commission chairperson Florence Jaoko said some suspects may interfere with ICC investigations if they continue serving since they hold senior positions in government.
She called on the six individuals to fully cooperate with the ICC.
Jaoko said that naming of the six individuals is a major step towards seeking justice for the victims of chaos adding that the move should be seen as a way forward of ending impunity in the country.
She said that renewed efforts by parliament to set up a local tribunal will not stop the ICC process but remains the best option.
The KNCHR chair appealed to parliament to put in place necessary legislation that will guide implementation of the new despite the Ocampo list fury.