BELFAST (Reuters) - Britain's Northern Ireland minister is set to call an early election in the province on Monday, a week after the resignation of Deputy First Minister Martin McGuinness effectively toppled its devolved government.

McGuinness stood down in protest at First Minister Arlene Foster's handling of a controversial green-energy scheme, risking political paralysis in the region as Britain plans its exit from the European Union.

Secretary of State for Northern Ireland James Brokenshire will be obliged to dissolve the assembly if McGuinness' Sinn Fein party, which has already begun picking election candidates, fails to name a replacement for him by a 1700 GMT deadline.

"Sinn Fein will not be nominating for the position of deputy First Minister and the agreements mean that the people must now have their say," Sinn Fein minister Michelle O'Neill said in a statement on Sunday.

Irish nationalists Sinn Fein, once the political arm of the IRA, has governed with its pro-British rivals, the Democratic Unionist Party (DUP), for a decade. They were voted back into power as the two largest parties just eight months ago.

McGuinness, who is to announce shortly whether he will lead Sinn Fein into the election after a break from some duties due to illness, has suggested the vote will be followed by lengthy renegotiations on the terms of the power-sharing government.

Power-sharing formed a key part of the 1998 Good Friday peace agreement, which ended three decades of violence between mainly Catholic Irish nationalists seeking a united Ireland and Protestant pro-British unionists wanting to remain part of the United Kingdom. Some 3,600 people were killed in those years.

Northern Ireland is widely seen as the part of the UK most exposed to Brexit because of the prospect of checkpoints being reinstated on its land border with the Irish Republic. Attempts to rebuild power-sharing will likely begin just as British Prime Minister Theresa May begins exit talks with the EU.

A failure to form a new ruling executive after the elections also risks the first suspension of the province's political institutions in 15 years and the return of its 1.8 million people to direct rule from London.

"What I'm focused on is that we maintain the institutions. This is really significant. To be absolutely straight ... I am not contemplating alternatives to devolved government in Northern Ireland," Brokenshire told the BBC on Sunday.

(Writing by Padraic Halpin in Dublin, additional reporting by Will James in London; Editing by Tom Heneghan)