Parliamentary opposition parties say they remain amenable to working with the government to constitute an independent inquiry to investigate death-squad allegations against Minister Ronald Garjaj.
"We stand ready to honour our undertaking to assist the government in generating the terms of reference for a credible inquiry," the PNCR, WPA and ROAR Guyana Movement said in a joint statement after a meeting on Wednesday at the Georgetown Club.
The implications of the security crisis on the election process were also among the issues discussed.
The parties expressed concern over the lack of progress in the review of the constitutional arrangements for new elections in accordance with the understandings of the constitutional review process. An agreement is still to be reached on electoral processes for the next local government and general elections.
One month ago, President Bharrat Jagdeo announced his decision to set up a Presidential Commission of Inquiry to investigate Home Affairs Minister Ronald Gajraj's alleged involvement in organised killings.
Under its terms of reference the commission is to determine whether there is credible evidence to support allegations that the minister had any involvement in extra-judicial killings.
The parties maintained their original position on the commission, which they say falls far short of what is required to resolve the allegations and the implications.
They have also panned the terms of reference and are also critical of the continued presence of Gajraj at the Home Affairs Ministry, which they say undermines the president's proposals.
But they reaffirmed their willingness to do everything that is necessary to ensure that all legislative action is put in place to facilitate an independent inquiry in Parliament.
"We are still hopeful that good sense will prevail and that the commissioners named will recuse themselves from this farcical exercise and the government will allow good sense to prevail and seek consensus support for opposition and civil society for a way forward in this matter."
They have also agreed to write to the UN seeking support for the country, reasoning that the deteriorating security and political situation has moral and political implications for the international community.
The opposition groups also pledged to continue their support for civil society's political campaign in this matter and to ensure that the people are kept aware of the issues.
President Jagdeo named Justice of Appeal Ian Chang as chairperson of the commission, which is to also include retired Major General Norman McLean and ex-Deputy Commissioner of Police Ivan Crandon.
But Crandon is also Chairman of the Police Service Commission and under the Constitution is precluded from holding a public office.
This is an objection that was raised by the Guyana Human Rights Association (GHRA), which has also argued that his appointment may be a conflict of interest since the commission may be required to examine members of the police force as part of its mandate.
The government maintained up to last week that President Jagdeo is being advised on the legal implications of Crandon's appointment, which he has said he is willing to reconsider.