Taoiseach Enda Kenny was among the first EU leaders consulted by the new British Prime Minister Theresa May on her first day in office.
Mrs May took over from David Cameron, who resigned following the Brexit referendum vote for Britain to leave the European Union.
Ireland is Britain’s fifth largest trading partner and both Mr Kenny and Mrs May are keen to ensure that the relationship between the two countries is not damaged by the Brexit decision.
The telephone conversation between the two was said to be cordial with the Taoiseach wishing Mrs May the best of luck and welcoming her commitment to make the United Kingdom a country that works for everyone.
They both agreed that the strong collaboration between their two countries should continue and the Taoiseach offered to visit London soon for talks on how they could best work together to achieve this.
The Prime Minister explained that she would need some time to prepare for the complex Brexit negotiations and spoke of her hope that these could be conducted in a constructive and positive spirit.
In addition to trade, Mr Kenny will also seek reassurances about the border with Northern Ireland and implications for the Peace Process.
A Downing Street spokesperson said Mrs May also took congratulatory calls from the German Chancellor Angela Merkel, and President Hollande of France
Mrs Merkel congratulated the Prime Minister on her appointment, invited her to visit and said that she hoped to see her at the G20 in September.
They agreed that they wanted to establish a constructive relationship, recognising the importance of close co-operation between the UK and Germany.
President Hollande also called to offer his congratulations and to wish the Prime Minister well in her new role.
They discussed the importance of the bilateral relationship, particularly security and defence co-operation and also the joint work on border controls in Calais.