"We look forward for Mr Boochani having the opportunity to permanently resettle in a third country as soon as possible, wherever that may be," the statement by Senator Keneally read.
"Labor has been calling on the third term Morrison Government to resettle eligible refugees in PNG and Nauru for close to six years."
However, Boochani has panned the remarks, describing them as unacceptable.
"You exiled me to Manus and you have supported this exile policy for years," the Kurdish refugee said.
"I don't need you to welcome resettlement for me in a third country."
The asylum-seeker advocate and award-winning author is now calling on Labor to do more to assist others who have faced similar challenges.
"If you are honest, do something for others who are suffering in PNG and Nauru," he wrote.
Boochani arrived by boat on Christmas Island in July 2013 and was sent to Australia's offshore detention facility on Manus Island in Papua New Guinea a month later, while under the administration of Labor Prime Minister Kevin Rudd.
It was Boochani's reporting and support of Kurdish independence which saw him seek asylum further abroad, amid fears of persecution in Iran.
A spokesperson for Senator Keneally has refused to comment on Boochani's reply.