The previous deadline of "early May" was abandoned after Prime Minister Theresa May called a snap election for June 8, as the parties acknowledged that the campaign could make it difficult to reach compromises.
"If an agreement is not possible before the general election, it is right that we provide flexibility for an incoming government to act in the best interests of Northern Ireland and the space for the parties to conclude a deal," James Brokenshire, Secretary of State for Northern Ireland, said after introducing the new legislation.
The new legislation will also let a gridlocked Northern Ireland collect the household tax payments that are needed to finance local council services.
The power-sharing executive is the cornerstone of a peace process that ended three decades of violent conflict between Catholic Irish nationalists and Protestant British unionists.
It fell apart in January when the republican Sinn Fein party pulled out after months of bad blood between them and the pro-British Democratic Unionist Party (DUP).
An initial three-week deadline for Sinn Fein and the DUP to resolve their differences passed with no resolution and the British government granted more time.
If the feuding parties are unable to form a semi- autonomous government in Belfast, a new election will be called or the province will be fully governed from London, the British government has warned.
Negotiations so far have only underscored the disagreement over how to deal with legacy issues from the decades of violence before 1998, including a bill of rights and the status of the Irish language.
Northern Ireland will have the only land border between the UK and EU territory, and is highly dependent on cross- border trade with the Republic of Ireland.
During a visit to London today, Sinn Fein's deputy leader Mary Lou McDonald said designated special status for Northern Ireland within the EU was the only way to protect Ireland's economic interests.
"There is deep concern that the draft EU Council resolution is so weak in relation to Ireland and, without a major change of approach from Taoiseach Enda Kenny, we are on route to a bad deal for the peace process, a bad deal for our agriculture sector and a bad deal for the wider economy," she said.
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