David Cameron has told Taoiseach Enda Kenny he "admires very much" the economic decisions being taken in Ireland.
As Mr Kenny made his first formal trip to Downing Street, the Prime Minister pledged to work "extremely closely" with Ireland as the two nations battle to rebalance their finances.
Mr Cameron said: "It's great to have the Taoiseach here. Enda Kenny and I will work extremely closely, I think we have a lot of closely-shared interests.
"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."
Mr Kenny said: "The links between Ireland and Britain on trade and social contact is something we want to work on."
He said Ireland faced an "enormous challenge" and his government had a mandate to get the country's finances under control.
"Obviously the people want that sorted out and we want to do that with a sense of courage and fairness, and to rebuild connections with our colleagues in Europe, and particularly with Britain," he added.
Mr Cameron 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.
Speaking outside No 10, the Taoiseach thanked the UK for its £3.25 billion bilateral loan to Ireland.
"We were very grateful to receive that," he said. "We didn't discuss it in any detail but in the context of the loan that Ireland has received from the IMF-EU package."
Asked whether he had asked the Prime Minister to cut the interest rate on the British loan, he said the matter had not been raised.
"The Prime Minister made the point that it was put through very quickly by Britain here and there wasn't any difficulty with that," he said.
"We didn't discuss the possibility of a reduction in the interest rate in that loan today. We did discuss the ongoing situation as far as Germany and France and other countries are concerned and on rebuilding our reputation with other countries.
"The decision was that the Minister for Finance should carry forward the question of an interest rate reduction.
"And I think when Europe sees the seriousness of intent of the new Irish Government to deal with our problems, hopefully that can be resolved."
Mr Kenny said the "vast majority" of Irish people would welcome the Queen's visit to Ireland on May 17-20 - the first visit by a British monarch in 100 years.
But he warned that there may be some protests, as the date of her visit clashed with the anniversary of the Dublin and Monaghan bombings that killed 34 people on May 17 1974.
He said the Queen's itinerary - which includes a visit to Dublin's Garden of Remembrance, which honours those who fought for Irish freedom - was "sensitive" and "well thought-out".
But he added: "I reminded the Prime Minister that because the date of the arrival of the Queen coincides with the date of the Dublin-Monaghan bombings, then obviously there may be a small measure of protest arising from that."Reuse content