Charlie Flanagan said an important breakthrough was made on Friday morning and he detected a determination on everybody's part to reach an agreement.
The talks are on flags, parades, the legacy of the Troubles and welfare.
Mr Flanagan predicted that an agreement was possible if not on Monday, then "a short time after".
However he accepted that everyone was waiting for Prime Minister David Cameron's response to the five Northern Ireland Executive parties' proposals on finances.
The five main parties have asked the UK government for £2bn in loans and extra funding over a 10-year period, the BBC understands.
In an interview with the Irish state broadcaster RTÉ, Mr Flanagan said there had been progress on Troubles legacy issues as well as finances on Friday.
However, he added that "nothing is agreed until everything is agreed".
In a statement on Friday night, Sinn Féin's Martin McGuinness said efforts to achieve a comprehensive agreement have so far been inconclusive.
"Progress has been made and today the five parties have agreed a set of proposals regarding public finance that would enable the executive to use its powers to protect the most vulnerable, and to invest in building peace and reconciliation and welfare safeguards.
"These proposals require additional financial support.
"There has yet to be agreement on the outstanding issues of identity, parades and the legacy of the past," Mr McGuinness added.
The five main parties' request to the UK government includes a peace investment fund and cash to pay for public bodies that would examine the legacy of the Troubles.
They have asked the Treasury to write off £214m in fines imposed on the executive for its delay in implementing welfare reform.
The negotiations continued late into the evening again but finished shortly after 22:00 GMT.
Speaking at Stormont, Mr Flanagan said he and Northern Ireland Secretary Theresa Villiers would resume talks on Monday.
The Irish foreign minister has said he is hopeful that there will be a deal in Northern Ireland's cross-party talks early next week.