Britain's queen was one of the first heads of state to send best wishes to Ireland's new president.
A Buckingham Palace spokeswoman confirmed that she had sent private messages of support to Michael D Higgins.
The royal also paid tribute to former president Mary McAleese, who welcomed her to Ireland in May for the historic first visit by a British monarch to the Republic.
"The queen has sent her best wishes to both of them and mentioned the historic visit to Ireland earlier this year," said a palace spokeswoman.
Elsewhere, the president of the European Commission, Jose Manuel Barroso, also sent a message of congratulations.
"On behalf of the European Commission, I would like to offer you my warmest congratulations on your inauguration as President of Ireland," said Mr Barroso.
"You are taking office at an important time, as Ireland takes resolute action to address difficult economic circumstances and in doing so, is setting an example for other countries facing similar challenges."
Mr Barroso said he looked forward to meeting Mr Higgins during the Irish presidency of the European Union in 2013.