Mr Durkan obtained the commitment via a written Assembly question.
He has been campaigning for the expansion of the scheme to include support for the parents of sick children from low-income households.
Said the Foyle MLA: “This is a small step but a positive one nonetheless for parents of sick children who have been impacted by the added financial burden of travel costs.
“I’m grateful that after initially rejecting my proposal last year, the Health Minister has reconsidered and has now committed to progressing a review into the expansion of the Hospital Travel Costs Scheme to include low-income families with sick children attending hospital appointments or in need of inpatient care.
“For any parent, the prospect of their child being unwell or requiring a hospital stay is extremely worrying in itself, but for many parents of children with long-term health conditions, travel costs to avail of specialist medical treatment can prove costly.
“In such instances the family of young inpatients are excluded from the Hospital Travel Costs Scheme.
“However, after identifying this significant gap in support and subsequent successful lobbying of the Health Minister, I’m pleased that steps are being taken to resolve it.
“Opening up this scheme is even more important now given the financial climate and I’ve no doubt it will prove to be an important lifeline for struggling families.
“Securing such a provision would take pressure off parents at an already difficult time and I look forward to working to secure this overdue support to benefit families across the North.”