Stormont has been in political deadlock since the DUP and Sinn Féin were once again returned as the largest parties in an election at the start of March.
That followed a breakdown between the governing parties in January over a renewable heating scandal, which saw Sinn Féin pull out of the power-sharing executive.
The republican party have vowed not to work with their unionist counterparts until a full inquiry into the project is conducted, while a series of policy clashes on issues such as legacy and the Irish language between the parties are recognised as other barriers to the formation of a government. As a result of this, civil servants have taken on responsibility for public spending decisions.
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While roundtable talks that have been ongoing over the last ten days are to “pause” for Easter, the Northern Ireland Secretary said the UK and Irish governments would continue to seek progress.
The previous deadline had been set at 18 April but has now been extended.
Brokenshire said there had been “a lack of agreement between the parties on a small but significant number of issues”.
The restoration of devolved government remains achievable, but more time and a more focused engagement on the critical issues are required, he said.
“The parties will have a final opportunity after Easter to reach agreement, building on the discussions which have taken place over the past six weeks.”
He added that British civil servants would continue to prepare for the scenario that an executive would be created in early May.
“The parties mandated by that election still have a duty to provide the government for which they campaigned,” he added.
“I believe that the outstanding issues between the parties are surmountable, but if no executive is formed by early May, I will need to take further steps to ensure Northern Ireland has the political stability it needs.
“This is likely to mean, however undesirable, either a second election or a return to decision making from Westminster.”
Under the terms of the Belfast Agreement, Northern Ireland must be governed by a joint unionist-nationalist administration.
Until the collapse of the administration in January, the region was in its longest period of devolved government since before the Troubles.