Taoiseach Micheál Martin has said the DUP was wrong to place conditions on participating in the Northern Ireland Assembly.
The election was won by Sinn Féin in a historic victory, with the party overtaking the DUP to become the first nationalist or republican party to emerge on top at Stormont.
The unionist party, led by Sir Jeffrey Donaldson, has insisted that it will not form an Executive until issues with the Northern Ireland Protocol are resolved.
Mr Martin said the people of Northern Ireland wanted their political representatives to fulfil their mandate.
The DUP should "take their seats and get on with it" he told RTÉ radio's Morning Ireland.
The election had been fought on issues that were impacting people’s lives such as the cost of living, housing and health. Political parties could lose out if they did not address these “bread and butter issues” he warned.
Talks between the UK and the EU on the Northern Ireland Protocol should now intensify, said Mr Martin. The UK assessment of the situation had not been fair on the EU, he added. There had been “a fair deal of movement” by the EU, but every time the EU displayed any flexibility, it was not reciprocated and that had made them cautious.
The Taoiseach added that the British government wanted to bring the issue to a conclusion, “they want to get Brexit done”, but the ongoing issue of the Northern Ireland Protocol showed that “Brexit isn’t done”.
The EU was prepared to engage, but there needed to be an indication that there was a mood to resolve the issues, he said. There could not continue to be one concession after another by the EU.
The northern secretary, Brandon Lewis, is due to meet the leaders of the main Stormont parties later on Monday and will also speak to the Minister for Foreign Affairs, Simon Coveney.
Mr Martin said he believed that a compromise could be reached with the DUP, but that the DUP would need to be prepared to accept the politics of the situation.
When asked about a call from Sinn Féin leader Mary Lou McDonald for the issue of a United Ireland to be discussed by a Citizens Assembly, the Taoiseach said that the issue had not been central to the election.
The clear message from the people of Northern Ireland was that they wanted the institutions to work and to have a fully working Assembly. They wanted action on issues like education and health.
There needed to be an evidence based approach “about sharing this island together” and there should be a focus on making the Good Friday Agreements institutions work. The Citizens Assembly was not the way to proceed.