Deputy First Minister Martin McGuinness of Sinn Féin wants to press ahead with the transfer of political responsibility for justice and policing matters.
However, First Minister Peter Robinson is not prepared to support devolution because of concerns about the level of support for it in the unionist community, and reservations about how it will be funded.
Mr McGuinness has accused the DUP of holding back important parts of the Good Friday and St Andrew's agreements.
Gordon Brown has already held several meetings with Mr Robinson and Mr McGuinness to discuss the issue. At the Labour party conference on Monday, he said he would like to see devolution go ahead within months.
Today, Northern Secretary Shaun Woodward said significant new investment from the US was dependent on devolution going ahead.
