Peter Robinson and Martin McGuinness are to be nominated as first and deputy first minister at Stormont later.
In a statement on Wednesday, they said they "look forward to working together after we have been nominated as first minister and deputy first minister.
"We recognise there are outstanding and unresolved issues which have been raised with the prime minister and which require urgent attention."
These issues are to be discussed with Gordon Brown on Friday.
There had been speculation Sinn Féin would not renominate Mr McGuinness when Ian Paisley stands down.
"I am very pleased to say that I will be nominating Martin McGuinness as deputy first minister," party leader Gerry Adams said in a statement on Wednesday evening.
"There are a number of outstanding issues from the St Andrews Agreement to be implemented. These include the transfer of power on policing and justice and an acht na Gaeilge (Irish language act).
"These issues must be resolved satisfactorily if we are to build on the undoubted progress that has been made in the course of the past 12 months."
Prime Minister Gordon Brown said he has invited Mr Robinson and Mr McGuinness to Downing Street on Friday.
"On the agenda will be various urgent issues, including the forward investment strategy for Northern Ireland, the economic situation, devolution of policing and justice, continuing concerns around paramilitary organisations, parades, sites, the Irish language and education, and the putting in place of a process to deal with them.
"I look forward to my continuing involvement with the first and deputy first ministers," Mr Brown said.
"I remain committed to the continuing implementation of the St Andrews agreement and to helping the parties to address those issues that have been raised with me and require resolution."
The assembly is to hold a special sitting on Thursday afternoon to deal with the nominations.
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