Gerry Adams has called for a British/Irish intergovernmental conference on Northern Ireland.
British Prime Minister Theresa May has said Stormont budget legislation will be taken forward at Westminster on Monday after endless talks between Sinn Féin and the DUP failed to clinch an agreement.
She denied it was an indication of direct rule.
The two largest parties have been deadlocked for months over issues including an Irish Language Act and their leaders held conversations with Mrs May on Friday.
Sinn Féin president Mr Adams said: "We also told her that direct rule was not an option and that she must look to the provisions of the Good Friday Agreement for the establishment of an intergovernmental conference involving the Irish and British governments.
"In the absence of the institutions the two governments must implement those outstanding rights issues."
The Prime Minister's spokeswoman said she had explained how the UK Government will reluctantly be taking forward legislation for a Budget Bill on Monday, to ensure that in the absence of an executive, public services in Northern Ireland have the resources they need to operate.
She added: "The Prime Minister made clear this was absolutely not an indication of direct rule but it was necessary to enable the Northern Ireland civil service to allocate funds for key public services while talks between the parties continued.
"There was agreement on the importance of devolved government being returned to Northern Ireland for the benefit of all communities and the Prime Minister said that the UK Government would continue to work, alongside the Irish Government, with the parties in reaching a successful outcome."