The new Secretary of State has said he wants to "deliver enough pressure" to restore Stormont power-sharing and resolve issues with Brexit's Northern Ireland Protocol.
Chris Heaton-Harris held talks with Sinn Féin and the DUP during his first visit to Northern Ireland since his appointment on Tuesday by Prime Minister Liz Truss.
Sinn Féin vice-president Michelle O'Neill said people in the region "desperately" need an Executive and the British government should "stop pandering to the DUP".
Read more: Prime Minister Liz Truss determined to restore 'balance' between Northern Ireland communities
DUP leader Sir Jeffrey Donaldson hit back, saying that unlike now there were no caretaker ministers in post when Sinn Féin previously brought down power-sharing over the RHI controversy.
He added: "It's time Sinn Féin grew up when it comes to respecting the UK government and the mandate that we have to deliver a solution on the protocol."
The Stormont institutions have not been fully functioning for months due to the DUP blocking their re-establishment in protest against the protocol.
The post-Brexit deal with the European Union has angered unionists for introducing new checks on goods moving between Great Britain and Northern Ireland.
Mr Heaton-Harris said restoring devolved government is his priority, and he plans to meet with the other party leaders in the coming days.
He did not take questions from journalists in Dungannon, Co Tyrone, as he met with Sinn Féin representatives.
But the Secretary of State said: "I am looking forward to delivering enough pressure so we can get the Executive up and running, solve the problems of the protocol, and some of the more useful domestic things I can do to help people here in their everyday lives."
Ms O'Neill welcomed his comments on his determination to see the Executive restored, but said the "proof of the pudding will be in the eating".
She said: "I took the opportunity to make it very clear to him what my priorities are. Number one, getting an Executive up and running again.
"The public desperately demand that, they need that to help them through this cost-of-living nightmare that people are facing."
Ms O'Neill added: "They need our help and I want to be in an Executive, working with others to get support directly out to people.
"We made the case strongly that this situation is no longer tolerable, they need to stop pandering to the DUP."
Ms O'Neill said she stressed with the new minister that the protocol is "here to stay".
"We need an agreed way forward, we do not need more unilateral action, what we need is a negotiated way forward within the framework of the protocol."
Speaking later in Belfast ahead of his meeting with the Secretary of State, Sir Jeffrey said "decisive action" was needed to address problems with the protocol.
The DUP leader said the Protocol Bill making its way through Parliament presents an "opportunity for a solution".
Sir Jeffrey added: "Let's get this done, let's get the protocol sorted out, let's see Northern Ireland's place within the United Kingdom respected and restored, and then we can get on with the business of fully restoring the political institutions.
"In the meantime, let me be clear: my party will work day and night to ensure at Westminster and through our ministers at Stormont that people get the help they need, households and businesses alike in Northern Ireland get the support that they require to help with rising energy costs and to meet the cost of living at this time."
Mr Heaton-Harris succeeds Shailesh Vara, who had been Secretary of State for just 61 days after Brandon Lewis resigned during the turmoil that ended Boris Johnson's premiership.
Steve Baker replaced Conor Burns as minister of state in the Northern Ireland Office.
Both Mr Heaton-Harris and Mr Baker are former chairmen of the European Research Group of pro-Brexit Conservative MPs.
Sir Jeffrey welcomed the appointment of both ministers.
He said: "I believe that both of these ministers understand the nature of the difficulties that we face at this time, the challenges that we need to overcome."
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