Dame Lowell has also warned that she will no longer respond to any further requests for interviews or comments.
Her refusal to appear before MPs has been branded "disgraceful" and an "astonishing response" from a paid public servant, by Yvette Cooper, chairman of the home affairs select committee.
Ms Cooper said: "Dame Goddard has been paid significant amounts of public money to do an extremely important job which she suddenly resigned from, leaving a series of questions about what has been happening over the last 18 months and why the Inquiry got into difficulties,” said Cooper.
"Yet rather than give oral evidence to answer these questions she is relying on the fact that she is out of the UK to avoid the requirement to give evidence to Parliament.