SDLP leader Colum Eastwood is proposing the temporary suspension of the petition of concern as a way of restoring power-sharing at Stormont.
He said the death of Lyra McKee must be a turning point in Northern Ireland and politicians had a duty to respond to the public's wishes and act.
The petition of concern has most controversially been used by the DUP to stop same-sex marriage. It can be brought by 30 or more MLAs and requires a weighted majority to pass legislation.
Mr Eastwood said that pausing it would give enough space to get the Assembly and Executive up and running.
Ms McKee was shot dead by a New IRA gunman in Londonderry last Thursday night. A priest at her funeral called on the political parties to urgently end the stalemate at Stormont.
Mr Eastwood said: "We must listen to the public and act.
"There is a simple truth to be faced - politics here has failed. That truth means it is our responsibility as political leaders to fix it.
"We have been casual with our peace and we have forgotten our primary purpose.
"Today, the SDLP is proposing the suspension of the petition of concern mechanism for the remainder of this Assembly in order to legislate for rights and for all of our futures through the democratic mandate handed to us by the people of Northern Ireland.
"We are also proposing that while the temporary suspension takes place, a meaningful review of the petition of concern is conducted with experts to find agreement on how to protect rights and stop any future abuse of the mechanism."
The SDLP leader said the message from Ms McKee's death was clear.
"We can no longer allow the inactions of politicians to have dangerous effects on the streets, we can no longer allow the fact that we don't have a government to destroy our education system, to destroy our health service, to allow welfare cuts to be crippling our communities," he said.
"Condemnation is good, standing together is great, but doing nothing after that is meaningless.
"We should all be ashamed that we have created the context that allows things like that to happen."
Addressing the media at Stormont, he said he had spoken to Irish Foreign Minister Simon Coveney about his suggestion and he planned to talk to Secretary of State Karen Bradley.
"The SDLP has the legislation ready to bring progress and equality. We can begin to enact it on the Assembly's very first day back," he said.
The petition of concern was designed to ensure that contentious legislation can only be introduced with cross-community endorsement.
If one is brought in the Assembly, the support of 60% of MLAs voting on the issue is then required, including at least 40% of each of the nationalist and unionist designations present at the time.