Theresa May said her Government won't take on the role next summer following the Brexit vote
During her first conversation with Tusk since she became Prime Minister, she also warned the UK would need to "carefully prepare" for Brexit negotiations before triggering Article 50 - the process that officially starts divorce proceedings.
Tusk welcomed her "swift" decision on the issue and said that during their telephone call he had asked May for a "velvet divorce".
The Prime Minister travels to Germany this afternoon for what she has described as frank and open talks with her counterpart Angela Merkel.
Speaking ahead of the trip she said she was "determined that Britain will make a success of leaving the European Union" and her visits to Germany and France on Friday was to "forge strong working relationships".
The Taoiseach recently met with Merkel in Berlin to discuss Europe's future.
During the talks she said she wouldn't guarantee Ireland any special considerations, and that the Irish voice will be heard as much as every other voice.
Speaking on Newstalk Breakfast earlier this morning the leader of Fianna Fáil Micheál Martin said he believes things may be different behind the scenes and that Ireland will be given special treatment by Europe after Brexit.
"I think you need to be careful of the megaphone stuff and the public utterances at times of politicians."
Martin added that he was at a meeting recently with seven Prime Ministers from Europe recently and they all indicated that they were "very conscious of the special relationship relationship between Ireland and Britain and indeed of the Peace process and the impact of Brexit on that".
Additional reporting by IRN