Justice ministry: Villiers warns of fresh elections if deadline for appointment lapses
The Secretary of State, Theresa Villiers, has warned that fresh assembly elections will have to be held if a justice minister is not appointed by next Wednesday.
Ms Villiers said it would be a legal requirement.
She said she remained "hopeful" that the political parties could "resolve this issue".
The Alliance Party have been offered the justice ministry but have yet to decide whether to join the executive.
The party's ruling council is due to meet on Thursday to decide whether or not to do so.
Ms Villiers said she "very much" hoped that the Alliance Party would form part of the executive.
"I think David Ford has done an excellent job as justice minister and I'm sure one of his party colleagues would carry on with that excellent record if the Alliance chose to go into government," she said.
"I think they've played a very positive role in the executive over many years.
"I think it would be a pity if they were not part of the government, not least because it would make the executive less inclusive, so, certainly, when I saw the Alliance a couple of days ago I was warmly encouraging them to get involved.
"Yes, it's often tough on smaller parties in coalitions, but I believe that they will play a really positive influence as part of the executive if they take up the justice minister post."
Earlier, Deputy First Minister Martin McGuinness said the ministers of the new Northern Ireland Executive would be appointed next Wednesday.
The SDLP has yet to say whether it will join the executive.
The Ulster Unionists have already said they will enter opposition.
The majority of the posts in the executive will be filled by ministers from the DUP and Sinn Féin.
In 5 May's election, the DUP maintained the 38 seats it held in the last assembly, while Sinn Féin lost one and now holds 28.
The Ulster Unionists have 16 seats, while the SDLP have 12.
The Alliance Party secured eight seats during the election, meaning it does not have enough seats to automatically qualify for a ministerial department.