The father wants a stay on a decision made by a district court judge in childcare proceedings, allowing the children to be vaccinated.
He says that order should be postponed until a case, in which identical issues have been raised, has been ruled on by the Supreme Court.
The matter arises out of proceedings where the father of the two children, aged three and five, does not want them to receive MMR (measles, mumps, rubella) vaccinations because he believes they are harmful to their health.
The children's mother, who is estranged from her husband, wants the children to be vaccinated.
Last month the judge who heard the case made orders clearing the way for the children to receive the vaccinations.
Berenice McKeever, for the father, said the judge based his decision on a High Court ruling last May that a boy should be vaccinated in accordance with the wishes of his father. The boy's mother had objected.
That ruling was appealed to the Supreme Court where a judgment is pending, Ms McKeever added. Its outcome is extremely important to the current case, she noted.
Mr Justice Michael Peart granted lawyers for the father permission to bring his challenge against the district court judge's refusal to grant a stay.