Talks are set to continue over the summer
DUP leader Arlene Foster says no agreement has been reached to restore power-sharing at Stormont.
She said the talks will continue over the summer.
Both sides have been meeting to try and restore a power-sharing executive in the North.
Sinn Féin and the DUP are believed to be at odds over issues such as the Irish Language Act.
Mrs Foster said she was disappointed an agreement had not been reached, suggesting a deal will now have to wait until at least the autumn.
"We are going to keep working at it through the summer and hopefully we can come to an agreement later on in the year," she said.
"We are certainly up for an agreement, we are up for devolution."
Sinn Féin leader Gerry Adams said: "The reality is that the Sinn Féin electorate will not consent to being governed by the DUP on DUP terms.
"And we wouldn't expect the DUP electorate to be governed or to consent to be governed by Sinn Féin on Sinn Féin terms."
Sinn Féin leader in the North is Michelle O'Neill: "What this constitutes is a monumental failure on behalf of Theresa May - she has set back decades of work that has been done here throughout the years.
"And it's a consequence - as we all know - of the DUP supporting the prime minister and, in turn, the prime minister supporting the DUP".
Stormont has been without an executive since January.
Foreign Affairs Minister Simon Coveney travelled to Belfast on Tuesday morning for further meetings with the Secretary of State for Northern Ireland and the political parties.
Following the meetings, he said: "Having met the parties and the Secretary of State for Northern Ireland again this morning and talked through the detail of the outstanding issues, it now seems clear that agreement will not be forthcoming this week.
"The Secretary of State for Northern Ireland said yesterday that he stands ready to introduce the necessary legislation at Westminster to allow an executive to be formed once the necessary political agreement is reached between the parties.
"The Governments can support and encourage but, in the final analysis, it is only the parties themselves that can make an agreement with each other.
"All sides may now wish to reflect on how progress can best be made and I would encourage the parties to maintain dialogue with each other over the coming weeks.
"The Irish Government remains steadfast in our commitment to the Good Friday Agreement and to the success of its interlocking institutions.
"We are determined to play our part in supporting the resumption of the power-sharing government in Northern Ireland – and the sooner that happens the better."
The UK's Northern Ireland Secretary of State, James Brokenshire, said "gaps remain" between the two sides and that it was "clear" no deal would be struck soon.
He added: "All parties have, however, emphasised their desire to remain engaged and to find a way to return to and resolve these issues.
"The (British) government welcomes this and will do all it can to work with the parties to achieve a successful outcome. But we will not forget our responsibilities to uphold political stability and good governance in Northern Ireland.
"I will reflect carefully in the coming days on any further steps which may be required to support the continued effective provision of public services in Northern Ireland."
Additional reporting: IRN