There has been a mixed reaction to the announcement by Kenya's leader that this week's deadline for having a new constitution would be missed.
The issue of the president's powers is dividing the ruling coalition
One MP in the ruling coalition said that Kenya could be headed for chaos.
Other MPs praised President Mwai Kibaki's call for consensus. Both camps plan rallies at the weekend.
Mr Kibaki had promised to introduce a new constitution within 100 days of coming to power in December 2002 but the deadline then slipped to 30 June.
In a surprise television address on Monday, Mr Kibaki announced that the latest deadline would not be met.
He blamed a failure to agree on key issues and court cases but said he remained committed to having a new constitution.
The issue of whether to reduce presidential powers has split the ruling Narc coalition.
Elected president appoints PM
PM appoints cabinet
PM leads government and chairs cabinet
President remains head of armed forces
A leading member of the coalition, Raila Odinga, was promised the new powerful post of prime minister if he agreed to back Mr Kibaki's presidential campaign.
His Liberal Democratic Party (LDP) says it will demonstrate in the capital, Nairobi, on Saturday against the delay.
Police have also authorised a planned rally by Mr Kibaki's National Alliance Party of Kenya on the same day, raising fears of possible clashes.
Mr Kibaki said that a new parliamentary bill would be introduced to debate some compromise measures.
But the LDP's Otieno Katwang told the BBC's Network Africa: "They want us to retain the status quo, where the president has overwhelming powers."
"We are heading for anarchy and chaos," he said.