Gerry Adams has insisted that a deal can still be reached with the DUP to restore powersharing at Stormont.
He said that "some progress" was made with Arlene Foster's party before Sinn Fein decided to pull the plug on the latest phase of talks aimed at ending the political deadlock.
Mr Adams said there had been no point in continuing with the "ongoing verbal table tennis" with the DUP.
He said the process would be able to move forward with a British/Irish intergovernmental conference.
Mr Adams was speaking ahead of a meeting with Taoiseach Leo Varadkar on Wednesday evening to discuss the political crisis in Northern Ireland.
On Monday - in the absence of a Stormont agreement - a budget was brought forward at Westminster for Northern Ireland, leaving the future of devolution in a new phase of uncertainty.
Northern Ireland Secretary James Brokenshire moved the bill in the House of Commons, telling MPs he was "reluctant" to do it but the region would soon run out of funds with the political impasse entering its 11th month.
Mr Adams said Sinn Fein want the Stormont institutions back in place but it "has to be on the basis on which they were first established 20 years ago and under Martin McGuinness and Ian Paisley's leadership 10 years ago".
"The focus of the meeting (with the Taoiseach) is to ask (him) to be very firm with the British Prime Minister. She has a pact with the DUP", he said.
"The two governments under the terms of the Good Friday Agreement have the duty to convene the intergovernmental conference and we will be asking them to do that as a means of moving this process forward," the Sinn Fein leader added.
Mr Adams continued that while "some progress" was made during the recent talks process no agreement was reached on rights issues, such as a Bill of Rights, an Irish Lang Act, or marriage equality .
"These are very modest, standard rights in any society. The DUP are against rights. That is part of the conundrum. The issues aren't going away," he said.
Powersharing collapsed in January when then Deputy First Minister, the late Martin McGuinness, resigned in protest at how his counterparts in the DUP handled allegations of mismanaging a green energy scheme.
Since then, the DUP and Sinn Fein have engaged in multiple rounds of negotiations aimed at returning to government, all of which have failed to produce a deal.
The parties have said disagreements remain primarily around language and cultural issues, including whether to implement a standalone Irish language act.
Mr Varadkar and Irish foreign minister Simon Coveney met the Sinn Fein delegation.
Afterwards, an Irish government statement said: "The focus of the meeting was the current political situation in Northern Ireland, with a focus on how to reach a successful agreement to restore the Executive.
"The Taoiseach and the Minister reiterated the importance of effective power-sharing institutions in Northern Ireland for the overall implementation of the Good Friday Agreement, including the operation of the North South Ministerial Council, which also has a vital role in the context of Brexit.
"The Government has an unwavering commitment to the Good Friday Agreement, and is determined as a co-guarantor of the Agreement to secure the effective operation of all of its institutions.
"It will continue to engage intensively with the British Government and the parties in Northern Ireland in the coming weeks."