A dispute between Sinn Féin and the Democratic Unionist party (DUP) over an Irish-language act is threatening to derail the Northern Ireland assembly and executive. Arlene Foster formally resigned as first minister at 1pm on Monday but a standoff between the two biggest parties at Stormont is blocking her designated successor, Paul Givan, 39, from taking the post. If Sinn Féin and the DUP do not resolve the crisis within seven days – by 1pm on 21 June – the devolved power-sharing institutions will collapse and there will be an early assembly election. Edwin Poots, the DUP leader, appeared to harden his position on Monday when he declined to say if Irish-language legislation would happen during this mandate. “Time will tell,” he told BBC Radio Ulster. Sinn Féin has demanded the long-promised legislation as part of the price of rebooting the executive after a change of DUP leadership. It has accused Poots of acting in bad faith. Brandon Lewis, the Northern Ireland secretary, appealed for a smooth transition. “It is paramount that there remains a functioning executive that is able to work in the best interests of all the people and communities of Northern Ireland, delivering on the issues that matter to them most,” he said. History showed that political stability cannot be taken for granted, he said. “We all have a responsibility to protect it.” The crisis has flared on the cusp of a loyalist marching season that is tenser than usual because of loyalist and unionist anger over the post-Brexit Irish Sea border. Poots said peace would be “at risk” if Sinn Féin impeded the ratification of Givan, 39, a DUP assembly member Poots chose as first minister. “Setting pre-conditions is not appropriate, it’s not respecting someone’s mandate, and we cannot be in a circumstance where we have pre-conditions set for the selection of our first minister.” Street disturbances over Easter showed a fraught political climate, he told the BBC. “We saw riots on the streets of Belfast earlier this year. And I have serious concerns about the potential for conflict once again on our streets,” he said. “If Sinn Féin are going to play fast and loose with the very peace that people enjoy at this moment in time, then that is a very, very serious consideration for them to take. Hopefully they won’t.” An internal DUP revolt ousted Foster, the party leader since 2015, in April. She stepped down as party leader in May and ceased being first minister on Monday. In a statement to the assembly Foster urged all sides to stick to the 2020 agreement on language and culture. “It is only by respecting each other’s identity that we will move forward,” she said. Foster also said she would now spend more time with her family “whether they liked it or not”. Under Stormont rules, the deputy first minister, Michelle O’Neill of Sinn Féin, must also step down. If a new first minister and deputy first minister are not installed within seven days an election will be called. Sinn Féin has suggested it will not renominate O’Neill, thus blocking the elevation of Givan, unless it receives a commitment about the passing of Irish-language legislation next month. The party says the legislation was promised in New Decade, New Approach, the name given to a 2020 deal that revived Stormont three years after its collapse over other disputes. Neither Sinn Féin nor the DUP are believed to want an early election but they are under pressure to stand firm in the language dispute. Sinn Féin says legislation will show belated respect and equality for Irish culture. Many unionists, inside and outside the DUP, say nationalists have “weaponised” the language to undermine the region’s sense of Britishness. Delegations led by Poots and Sinn Féin’s chief negotiator, Conor Murphy, the Stormont finance minister, are to hold talks to try to break the impasse. Continued turbulence within the DUP likened to a soap opera – there are bitter clashes over personalities and styles – has weakened Poots. The latest member to resign is Ryan McCready, a Derry and Strabane councillor.