Taoiseach Leo Varadkar has met the Hungarian Prime Minister Viktor Orbán in Budapest.
Speaking afterwards at the Hungarian Parliament, the Taoiseach said they had a very good discussion and he was impressed by Mr Orbán's knowledge of Ireland.
He said it is important that Ireland develops new relations across Europe, especially in Eastern Europe.
Mr Varadkar expressed his appreciation for the support from Hungary in relation to Ireland's specific concerns on Brexit, particularly on issues around Northern Ireland.
He also said Europe needs to ensure a budget for its future, protecting policies like the Common Agricultural Policy and continuing to invest in structural funds.
Both countries are in favour of tax competition across Europe and they both believe countries should set their own corporate tax levels.
They discussed Europe's approach to managing migration, and the Taoiseach said Ireland and Hungary's views diverge on the issue.
Ireland supports the concept of burden sharing and Hungary does not.
Mr Varadkar said that he believes dialogue is the best way to bring the sides together.
Mr Orbán said they agreed the EU can be made stronger.
On taxation, he said reduction is a good policy and he would not like to see any countries being tied to a harmonised EU tax regime.
He said they touched on migration and he said he tried to make it clear why it is so important for Hungary, which is not against anybody but continues to be on the side of the rule of law, he added.
Both leaders also spoke about agricultural subsidies which Mr Orbán called an issue for both countries, saying it is the interest of Hungary that the policy does not change and subsidies should remain the same.
He said they also discussed Brexit and listened to the Irish considerations and that Hungary will support Ireland's position.
The visit is part of a continuing tour of European capitals since Mr Varadkar assumed office.
The trip was criticised by Labour Party leader Brendan Howlin, who said the Hungarian government is "anti-democratic and against EU values".
Mr Howlin has called for an explanation as to why the last-minute visit by the Taoiseach to visit the Hungarian leader was kept secret until now, and why the Dáil was not informed of this visit on 13 December in response to a parliamentary question.
He said that Ireland needs to know if the Government will challenge the policies that Hungary has been pursuing.
Tomorrow the Taoiseach will travel to Sofia to meet the Bulgarian Prime Minister.