The "Women on Waves" vessel was expelled from near Guatemala in February without carrying out a single pregnancy termination.
It had taken up position off Guerrero state, on Mexico's Pacific coast.
The "Women on Waves" group said in an online statement that it was offering "free legal medical abortions till 9 weeks of pregnancy" to women who needed them. It said its ship "has all required permits" and would receive women until Sunday.
It noted that Mexico permitted abortions in cases of sexual violence. Abortion is limited in other cases to different degrees across the 31 Mexican states.
The Dutch group has previously sent its ship to waters off Ireland, Poland, Portugal and Spain.
In a media conference given in the Mexican coastal town of Ixtapa, "Women on Waves" president Rebecca Gomperts said access to safe abortions was a matter of "social justice" in Latin America, especially after the Zika crisis which increases the risk of birth deformities.
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