The prime minister has defended Secretary of State Theresa Villiers who has said she will be campaigning for the UK to leave the European Union.
Deputy First Minister Martin McGuinness has said Ms Villiers should resign.
SDLP leader Colum Eastwood also said Ms Villiers should step down if Northern Ireland voted to remain in the EU.
But speaking on Monday, David Cameron said she was doing an excellent job and she had made a personal decision over the EU referendum.
"She is exercising her ability to reach a personal decision and to campaign for Britain to leave the EU and that's absolutely right she is able to do that," he said.
"I think the key thing is everybody in Northern Ireland should make up their own mind based on the evidence and I look forward to coming to try to help persuade them to remain in a reformed EU."
The secretary of state has said Northern Ireland will remain in a strong position financially if the UK decides to leave the European Union.
Her stance has been supported by the Democratic Union Party, but criticised by Sinn Féin and the SDLP.
The referendum on whether the UK should remain in the EU is due to be held on Thursday 23 June.
Ms Villiers said: "Northern Ireland and the rest of the UK could flourish outside the European Union and indeed that's something that the prime minister also acknowledges.
"We give, at the moment - £19bn a year to the EU and so we could actually, if we left, we could still afford to fund every single one of those programmes and still have significant sums left over for other priorities in Northern Ireland."
She has argued that it is time for the UK to "take back control and restore the ability to make our own laws and control our own borders in this country".
However, a previous NI secretary, Peter Hain, said Northern Ireland could be "dragged back" if the UK left the EU.
Mr Hain, who was secretary of state from May 2005 until June 2007, said he was concerned about the impact on Irish border controls.
"We have a unique situation on the island of Ireland with a border that now exists constitutionally but, in practice, is invisible to the great benefit of people on the island of Ireland, north and south," he said.
"I do not think that the existing border arrangements would be sustainable if we left the EU and that would have all sorts of very serious consequences for the peace process."