They also said that they will hold both the Irish and Egyptian governments responsible for anything that may happen to him.
Mr Halawa was detained in a mosque in Cairo as the Muslim Brotherhood held a “day of rage” over the removal of president Mohamed Morsi in August 2013.
He is being tried with hundreds of other protestors but the trial was adjourned for the 19th time last month.
“Ibrahim is dying and we as a family will hold both governments responsible for anything [that might] happen to him.
“We’re running out of time. We urge the Taoiseach to at least secure his release before it’s too late,” the family said in a statement.
They also referred to the release of Mr Halawa’s former cellmate, Australian journalist Peter Greste, freed after his government applied pressure on the Egyptian administration.
“Former cellmate Peter Greste’s government was able to secure his welfare and release for the period he spent in prison,” read the Halawa family statement.
“I am shocked that the Taoiseach can’t at least secure his welfare nor his conditions. Securing Ibrahim’s welfare means ensuring that he is placed in the best conditions possible,” it continued.
However, the Department of Foreign Affairs said yesterday Irish embassy officials in Egypt met with Mr Halawa on March 1 for 40 minutes. A spokeswoman also detailed an “exceptional” number of meetings between Irish and Egyptian authorities.
“The Taoiseach and Minister [for Foreign Affairs] Flanagan have been working continuously to support efforts to secure Ibrahim Halawa’s early return to Ireland.
"The Taoiseach has had a number of direct and personal contacts with Egyptian President el-Sisi, in face-to-face meetings, by telephone and through written correspondence,” the spokeswoman said.
“Minister Flanagan has been in regular contact with Egyptian foreign minister Shoukry on the case, and met him again on Monday March 6.”
Mr Halawa, meanwhile, has written several letters from prison about the treatment he has received. He has also been on hunger strike.
A delegation of eight TDs visited the now 21-year-old Ibrahim in January and also met the Egyptian president.