They vowed to stay put until Mr Muturi consults their leaders in the House dominated by the ruling Jubilee Alliance.
The House was expected to debate the laws and regulations that will guide the 2017 General Election.
Cord lawmakers paralysed business at the National Assembly for over two hours on Tuesday to protest a special sitting called by Speaker Justin Muturi.
The MPs blocked Mr Muturi from accessing the chambers, saying the 9.30am sitting was illegal since their House leadership had not been consulted.
“The gazetted time for this sitting was 9.30. Its way past that time,” Kisumu West MP Olago Aluoch, Ford-Kenya, said.
“We will not allow Jubilee to sneak in the Mace (the House’s symbol of authority). The only sitting that can now be properly constituted is the one at 2.30.”
Jubilee and Cord are fighting over proposed amendments to the Elections (Amended) Act and other elections regulations.
While Jubilee Alliance wants the law changed to be in line with “reality”, Cord wants it to remain in its current form and accuses the Uhuru Kenyatta-alliance of harbouring a sinister motive.
The laws were agreed upon by members of the Justice and Legal Affairs Committee as part of election reforms ahead of the polls.
At the centre of the debate is the proposal by the Samuel Chepkong’a committee to amend the Elections Act and provide for a manual backup system for the voting, transmission and tallying of election results.
The new subsection 14b(1) reads: “Notwithstanding the provisions of sections 39 and 44, the (electoral) commission shall put in place a complementary mechanism for identification and transmission of election results that is simple, accurate, verifiable, secure, accountable and transparent to ensure that the Commission complies with Article 38 (2) and (3) of the Constitution.”
The proposed amendment goes ahead to provide that if technology fails, the manual system shall be used to identify voters and transmit results. In subsection 14b(2), it proposes: “The commission shall use the complementary mechanism referred to in sub-section (1) for identification and transmission of election results only where the technology initially deployed fails.”
Other areas of concern with the amendments is the increase of the number of voters in a polling station from 500 to 700, removal of education qualifications for aspirants and the deadline for compliance with the Campaign Financing Act.
The MPs’ blockade forced Mr Muturi to retreat and was said to be holding a meeting with the House leadership on the row.
Majority Leader Aden Duale also held a closed-door meeting with Jubilee and Cord MPs at the dining room that involved a presentation from the IEBC to convince lawmakers of the need for the proposed amendments
It was after their meetings that the sitting began at 12.30pm, with House orderlies outmanoeuvring MPs led by Kakamega Senator Boni Khalwale who attempted to block the entry of the Mace.
During the heated debate, the Mace became the most protected asset of the House with a guard on each side.
There was a heavy police presence at Parliament Buildings, with officers blocking cars from passing through Parliament Road.
MPs and journalists forced to walk to the House as members of the public were locked out.
Cord leader Raila Odinga faulted the Jubilee government over what he termed “attempts to intimidate the opposition” by deploying security personnel around Parliament ahead of special session.
The move, he said, is a clear attempt to scare away the opposition MPs who had vowed to shoot down the amendments of some electoral laws.
“I have received information that GSU personnel were deployed around Parliament as early as 6am to scare away opposition MPs. This is unacceptable and can only be done by a regime that is in panic mode,” he said.
Speaking at a Homa Bay hotel during a meeting with elders from the Luo community, Mr Odinga said the deployment an indication that President Kenyatta had already sensed defeat in the 2017 polls.
“Even if you deploy a million security officers, this will not deter the opposition legislators from achieving the goals of scuttling attempts to alter electoral laws,” he said.
Mr Odinga assured the local business community that his government will improve a business environment.
He also defended the county governments against accusations of delayed payments by some contractors.
“We must know that funds from the Jubilee government trickle in bits making it difficult for effective operation by county governments,” he said.
Turkana Governor Josephat Nanok, who was among leaders present, renewed claims by the ODM leaders that Mr Odinga is best placed among Cord leaders to send Jubilee government home.
“Raila is the only leader within the coalition who does not only command respect across the country but is also accepted nationally,” he said.
Kenyans, he said, will only enjoy the fruits of devolution under Mr Odinga’s presidency.
“As the people of Turkana, we know of no other party than ODM and Raila as our leader,” he added.
The Turkana governor accused Jubilee government of intimidating him over the discovery of oil in his county.
“Jubilee government has persistently frustrated me because of the oil deposits in my county. I will, however, not be cowed and will remain steadfast in defence of my people,” he said.
Also present were governors Cyprian Awiti (Homa Bay), Cornel Rasanga (Siaya), Okoth Obado (Migori) and Kisumu Senator Anyang Nyongo among others.
Additional reporting by Maurice Kaluoch and Barack Oduor.