Mr Lewis said he wanted to see both unionist and nationalist parties nominate for the roles of first and deputy first minister “whatever the result” in May’s election.
Under Stormont’s powersharing arrangements, the first and deputy first ministers are chosen by each of the largest unionist and nationalist parties.
However, both the DUP and UUP have so far refused to say whether they would nominate for the deputy first minister role in the event that Sinn Fein emerged as the largest party and was entitled to the first minister position.
Linfield v Portadown Sunday clash: Breakers of the Sabbath will answer to God
Thousands expected to take part in 'Derry Day' this weekend
Esmond Birnie: The protocol is not as claimed boosting growth in Northern Ireland
Crawfordsburn Country Park: Five PSNI officers injured bringing crowd of 600 under control - two teens arrested - parents asked to know where their children are
NI Weather: 45 pictures of how we enjoyed wall-to-wall sunshine
Mr Lewis told the BBC Radio 4 Today programme: “The fundamentals of the Good Friday Agreement are the institutions.
“I would like to see all parties, both from the nationalist and the unionist side, be very clear that whatever the result in May, that they will nominate.
“I think the right thing for Northern Ireland is to have the devolved authority of the Northern Ireland Executive and the Assembly back sitting as quickly as possible after May 5 so they can get to grips with the issues.”
Mr Lewis also said he was disappointed that the DUP’s Paul Givan had resigned from the first minister role as part of his party’s protest at the Northern Ireland Protocol.
The step also removed Michelle O’Neill as deputy first minister and has left Northern Ireland without a functioning Executive, although other ministers still remain in post.
Mr Lewis said: “From my point of view, I think it is disappointing that Paul Givan resigned but I do hope that we can see the DUP re-nominate a first minister and get Stormont back up and running.
“The rules around Stormont have changed. Stormont has not collapsed, obviously the first minister and deputy first minister aren’t in post.
“The other ministers are in post, the Assembly can continue, a lot of the legislation that it is working its way through can continue and complete.
“One of the reasons I said we will not have an early election is, I think, it is important from a stability point of view for people to know that they can see that legislation completed and continue.”
He added: “This is an issue around the Northern Ireland Protocol and the DUP have made their decision based on that.
“The position the DUP have taken is that until they see positive steps forward in terms of resolving the protocol issues they will not re-nominate.
“We are focused on that, the Prime Minister is focused on that, (those) are the discussions we are having with the EU.”
Sinn Fein MP John Finucane told the programme that the decision of the DUP to bring down the Executive was “reckless and irresponsible”.
However DUP MLA for Fermanagh and South Tyrone Deborah Erskine responded later that DUP leader Sir Jeffrey Donaldson warned Mr Lewis and the Prime Minister last September that the Protocol was not compatible with devolved government.
“Not a single elected unionist in Northern Ireland supports the Protocol,” she said. “Progress is only made in Northern Ireland when a deal can command cross community support.
“Nationalists and republicans have made clear they would not accept a single extra camera on our border with the Republic of Ireland, therefore why should my unionist constituents have to tolerate the EU demanding them to open their suitcases when traveling from one part of the United Kingdom to another. Indeed, a recent EU report even claimed people should be charged for the checks. Imagine the outcry if anyone had to stop at Aughnacloy when crossing in to the South and open their luggage and pay for an EU official to check it.
“The Irish Sea border must go. Brandon Lewis knew that last September. Sir Jeffrey was reasonable. He gave space for talks but there was no sign of progress. If the Government want devolved government restored then they should legislate to remove the Irish Sea border.”