Mr Cameron was speaking during his first official meeting with Taoiseach Enda Kenny in Number 10.
The PM and Mr Kenny discussed economic and security matters during their half-hour meeting, as well as the Queen’s state visit to Ireland next month.
The PM said:
Obviously, with the economic situations in both our countries we need to work together very closely.
We’re both facing a situation where we need to see our economies grow, we’re dealing with deficits and debt. I admire very much the decisions you are having to take in your country.
Speaking alongside Mr Cameron, the Taoiseach said:
The links between Ireland and Britain for so many years - in trade, in business, in social contact - is something that we want to work on.
Mr Kenny also welcomed the forthcoming State Visit to Ireland by The Queen and praised the “well chosen” programme. The Queen will be the first reigning monarch to visit Ireland in 100 years.