The Women on Waves group has confirmed that no abortions will take place on the Aurora ship, which is docked at Sir John Rogerson's Quay in Dublin.
Kathleen O'Neill of the group's Irish office said two problems had arisen.
Firstly, the office had received about 80 calls from individuals, a figure she said they could not handle.
She also said that the failure to obtain a licence to perform terminations from the Dutch authorities could result in legal problems.
A yacht carrying an anti-abortion banner displaying the face of a child has been sailing up and down the Liffey this morning, but as yet, there have been no confrontations between pro and anti-abortion activists.