Kenyan Prime Minister Raila Odinga says fresh elections may be needed if a rift in the power-sharing government cannot be solved.
He wants to be put in charge of government business in Parliament, to replace Vice-President Kalonzo Musyoka. Mr Odinga and President Mwai Kibaki agreed to share power last year to end months of post-election violence.
But relations have soured and the two parties have held crisis talks.
Over the weekend, President Kibaki's Party of National Unity accused Mr Odinga's Orange Democratic Movement of "fomenting a coup".
The president's allies say he has the power to decide who should hold the crucial position of leading government business in the house.
The BBC reports the Speaker of Parliament is due to issue a ruling on Tuesday.
About 1500 people were killed and 300,000 forced from their homes after Mr Odinga's supporters said he had been cheated of victory in the December 2007 presidential election.
Former UN Secretary General Kofi Annan managed to broker a power-sharing deal in February 2008, which ended the violence.