British ministers have rejected claims that Sinn Féin’s election victory in Northern Ireland heralds the break-up of the UK, in spite of the nationalist party’s push for a referendum on a united Ireland within five years.

Brandon Lewis, Britain’s Northern Ireland secretary, on Monday begins the painstaking process of trying to coax pro-UK unionists to join the region’s government, which now has a pro-Irish unity party claiming the role of first minister for the first time.

Lewis is threatening to unilaterally rip up post-Brexit trading arrangements for Northern Ireland that are hated by unionists, in an attempt to bring the Democratic Unionist party — which finished second in Thursday’s elections behind Sinn Féin — into the region’s power-sharing executive.

But British ministers were adamant that Sinn Féin’s emergence as the largest party at Stormont did not make it inevitable that a referendum could soon be held on whether to transfer rule over Northern Ireland from London to Dublin.

“Sinn Féin haven’t gained seats,” Lewis told the BBC, noting that the 27 seats won by the party — long associated with the paramilitary Irish Republican Army — was exactly the same number as it secured in 2017, in the last round of elections.

He added: “We haven’t seen a growth in the nationalist vote and indeed the unionist vote is still larger and the number of seats held by unionist parties is still larger.”

Dominic Raab, the UK’s deputy prime minister, was asked whether the country was heading towards break-up, with nationalist parties now in charge of devolved governments in both Northern Ireland and Scotland. “I don’t think so,” he said.

Referring to the Northern Ireland elections, he added: “What I’ve noted is that 58 per cent of those voting in these elections voted for either those that support the union or don’t want to see constitutional change.”

British ministers have drawn some comfort from the rise of the centrist Alliance party, which identifies as neither nationalist nor unionist. It won 17 seats, compared with the DUP’s 25.

Mary Lou McDonald, president of Sinn Féin, said after the Northern Ireland elections that she believed a referendum on a united Ireland — a poll to be held on both sides of the border — “would be possible within a five-year timeframe”.

The Northern Ireland Act of 1998 requires the British government to allow a border poll “if at any time it appears likely” that a majority would express a wish for the region to leave the UK and form part of a united Ireland.

British ministers insist they want to negotiate changes with the EU to the so-called Northern Ireland protocol that covers the region’s post-Brexit trading arrangements, but they say time is running out.

UK prime minister Boris Johnson is drawing up legislation enabling Britain to unilaterally rip up parts of the protocol, which forms part of his Brexit deal with the EU.

The DUP is refusing to join the Northern Ireland executive unless the protocol is scrapped, which would mean the devolved government being unable to operate effectively and result in months of political limbo, and then potentially a fresh round of elections.

Lewis and Liz Truss, UK foreign secretary, claim the EU is being intransigent over the protocol, with Emmanuel Macron, French president, regarded in London as being the biggest obstacle to a compromise.

But Maros Šefčovič, the European Commission vice-president and lead negotiator on Brexit and the Northern Ireland protocol, said on Sunday that Brussels had already shown “a lot of flexibility by proposing impactful, durable solutions and we stand ready to continue discussions”.

He called on the UK to “dial down the rhetoric, be honest about the deal they signed and agree to find solutions within its framework”.

The US urged the UK and the EU to reach a compromise on the Northern Ireland protocol, saying Washington’s priority was protecting “the gains” of the 1998 Good Friday Agreement that ended three decades of armed conflict in the region.

The US state department said: “We recognise that there have been challenges over the implementation of the Northern Ireland protocol and that talks between the UK and EU to resolve these continue . . . 

“We urge the parties to continue engaging in dialogue to resolve differences and bring negotiations to a successful conclusion.”