But while Mr Martin insisted he was doing his best for 29-year-old Billy Burke, health officials and hospital representatives who met to consider his case ended their discussions without making any decision on his future.
Billy, who urgently needs a lung transplant operation, fears official inaction will kill him as he waits for resolution of the contractual row that has already been sapping his strength for an agonising 14 months.
"My situation is now terribly desperate," he wrote in a letter hand delivered to Mr Martin yesterday.
He accuses the hospital at the centre of the row of "recklessness" and "belligerence" and describes his dwindling faith in the Irish Government, which he once believed would not stand by and let him suffer.
Billy, who has cystic fibrosis, was put on the transplant waiting list four years ago at Freeman Hospital in Newcastle, England, which has a deal with the Department of Health to carry out surgery on Irish patients in return for getting first call on donated Irish lungs.
Last year, in a move questioned by Irish doctors, the hospital took him off its list after he contracted an infection but although a hospital in Manchester has offered to carry out the procedure, Freeman will not release organs to another transplant team.
A meeting took place in Dublin yesterday between representatives of the hospital and officials of the Department of Health and Eastern Regional Health Authority to review the controversial contract but while they discussed Billy's case, they refused to set aside the legalities and act to help him. As the meeting began, Billy's sister, Lisa Burke-Joyce, confronted Mr Martin, who was preparing to address doctors at the Irish Medical Organisation's annual conference in Killarney, less than ten miles away from the family's Killorglin home. She broke down in tears as she handed over her brother's letter, pleading: "Are you going to waste any more time?" Referring to Billy's isolation in a single room as he battles to prevent re-infection, she continued: "We're begging you. Billy has given a whole year of his life for this."
Family friend, Anne Foley, challenged Mr Martin to flex the same muscles he used when pushing through the smoking ban to break through the less formidable barriers to Billy's survival.
"You are powerful enough to make the country smokeless overnight.
"Can you save Billy's life? Are you powerful enough to do this?" she asked.
It has emerged Billy is just one of at least three Irish patients to have been refused transplants by Freeman Hospital in recent times, including one man who has already died.
Mr Martin said all that could be done for Billy, would be done, but he said the power to decide lay with the doctors involved. He also defended the arrangement with Freeman Hospital, pointing out that the number of lung transplants performed on Irish patients had quadrupled.
He admitted, however, that Billy's case had "raised issues around the agreement" and said it might be possible to revise it when the transplant unit at the Mater Hospital in Dublin begins performing surgery later this year.
Last night, Billy was not expecting to see that milestone. "If suitable organs are not made available to the hospital in Manchester immediately," he told Mr Martin, "I will die."