The Irish Family Planning Association (IFPA) says migrant women are facing "insurmountable" obstacles in trying to travel abroad for an abortion.
These include issues such as trying to find money to travel abroad or arrange travel documentation to leave and re-enter the country.
An audit of its services shows 26 women who were seeking asylum here or had other travel restrictions contacted the group for help in the year to the end of September.
At least five of these women continued with their pregnancy and parented against their wishes, it says.
The IFPA is warning that delays and obstacles have a significant impact on a woman's physical and mental health.
It has told the Irish Times the restrictions can be "impossible barriers" for many asylum seekers.
While figures from earlier this month show a British charity has helped more than 500 Irish women to secure terminations in England so far this year.
The Abortion Support Network gives advice by phone to women seeking terminations, and gives money to those who cannot afford to pay.
The body provided more than €50,000 in grants to Irish women last year.
The numbers contacting the charity have increased from 89 in 2010 to more than 500 this year.