The President, Mrs McAleese, talked to President Clinton, the British Prime Minister, Mr Blair, and the UN Secretary-General, Mr Kofi Annan, during the funeral of King Hussein, according to a spokeswoman.
Mrs McAleese, accompanied by the Minister for the Marine, Dr Michael Woods, her husband, Dr Martin McAleese, two officials from the Department of Foreign Affairs and her adviser, Ms Eileen Gleeson, arrived in Amman late on Sunday night.
At noon Irish time yesterday, Mrs McAleese was among a procession of heads of state past the coffin of King Hussein at the palace. She also joined other heads of state in the procession to the place of burial.
The spokeswoman for the Aras said Mrs McAleese did not attend the funeral as it was a "private ceremony only for Muslims". After the funeral, Mrs McAleese paid her respects to King Abdullah and his family at the palace, the spokeswoman said.
The Irish party, travelling on the Government jet, left Amman yesterday afternoon, and arrived in Florence. Mrs McAleese begins a five-day official visit to Italy today. She will deliver the Jean Monnet lecture at the European University Institute (EUI) in Florence and attend a dinner hosted by the institute president this evening.
Her audience with Pope John Paul II is due to take place in Rome at 11 a.m. on Friday. She is also due to meet the Archbishop of Canterbury, Dr Carey, at the Anglican Centre in Rome on Saturday before returning to Ireland.