The Prime Minister held a meeting with Taoiseach Enda Kenny in London on Monday, during which there was agreement on improving links between Britain and Ireland.
However the leaders continue to remain at odds over how the 1989 death of Mr Finucane, who was gunned down by loyalist paramilitaries, should be investigated.
The Finucane family want a Bloody Sunday-style independent inquiry into allegations of collusion between the killers and security forces - and are supported by Mr Kenny.
However David Cameron has ruled that out and instead offered an 18-month long QC-led review into the circumstances of the murder, with no participation from the family.
Speaking after Monday's talks at Number 10 Downing Street, Mr Cameron defended his stance.
He said: "It's not the nature of the review that matters - what matters is getting to the truth.
"I don't think it's necessary for us to have a lengthy, judge-led, judicial review, with all the problems and costs and expense and time that that takes."
Mr Kenny also vowed to stand by his position and pledged to continue making the case for a full review, adding: "I have a difference of opinion here with the Prime Minister".
The pair did agree that relations between the two nations have improved significantly in recent years, following on from the Queen's historic visit to the Republic in 2011.
A wide-ranging, ten-year co-operation deal was signed and Mr Cameron expressed "continuing and unqualified support" for the Good Friday Agreement.
He said: "We are determined not to roll back on our heels in this moment but actually roll up our sleeves and make the relationship mean even more."
Mr Kenny said: "It covers a very broad spectrum of reality here ... recognising that the relationship between Ireland and Britain is now at an unprecedentedly high level of co-operation and interaction in trade and business which is to the benefit of both."
However the leaders continue to remain at odds over how the 1989 death of Mr Finucane, who was gunned down by loyalist paramilitaries, should be investigated.
The Finucane family want a Bloody Sunday-style independent inquiry into allegations of collusion between the killers and security forces - and are supported by Mr Kenny.
However David Cameron has ruled that out and instead offered an 18-month long QC-led review into the circumstances of the murder, with no participation from the family.
David Cameron refuses to change his position on Pat Finucane review. Enda Kenny says he supports family call for judge led Inquiry
He said: "It's not the nature of the review that matters - what matters is getting to the truth.
"I don't think it's necessary for us to have a lengthy, judge-led, judicial review, with all the problems and costs and expense and time that that takes."
Mr Kenny also vowed to stand by his position and pledged to continue making the case for a full review, adding: "I have a difference of opinion here with the Prime Minister".
The pair did agree that relations between the two nations have improved significantly in recent years, following on from the Queen's historic visit to the Republic in 2011.
A wide-ranging, ten-year co-operation deal was signed and Mr Cameron expressed "continuing and unqualified support" for the Good Friday Agreement.
He said: "We are determined not to roll back on our heels in this moment but actually roll up our sleeves and make the relationship mean even more."
Mr Kenny said: "It covers a very broad spectrum of reality here ... recognising that the relationship between Ireland and Britain is now at an unprecedentedly high level of co-operation and interaction in trade and business which is to the benefit of both."
http://www.u.tv/News/Cameron-stands-by-Finucane-stance/151f88ff-d797-44ad-9792-48b75a651eed
