The ship provides medical abortions to women in countries where the procedure is banned.
How does it work?
The ship, operated by Dutch NGO ‘Women on Waves', picks up women on shore and brings them to international waters where local laws do not apply.
On board, women are given an abortion pill and remain under observation for a few hours before returning to land.
The procedure, also known as a medication abortion, combines two medicines, mifepristone and misoprostol, to end a pregnancy. It is more than 90 percent effective for women up to 10 weeks pregnant.
Why did Guatemala block it?
Abortion is banned in the country and it wants the ship to stay away.
"The military will not permit this group to carry out its activities in the country," Guatemala's military said in a formal complaint to the prosecutor's office issued on instructions from President Jimmy Morales.
Port officials have ordered the activists to stay on board their ship, saying they had not declared the motive of their trip and therefore could not come ashore.
The arrival of the ship also prompted fierce protests by Christian groups.
"They say they are fighting for life and human rights, but it looks like murder has become a human right," said a protesting seminary student from Cuba, Gil Hernandez.
Has this happened before?
Since it was set up in 1999, a Women on Waves ship has also visited Ireland, Poland, Portugal and Spain, prompting protests by pro-life groups in each country.
Women on Waves argued on Thursday that "especially at the dawn of the Zika crisis, access to safe abortion is fundamentally an issue of social justice."
Its founder Rebecca Gomberts confirmed that the Guatemala trip was the first since a 2012 campaign in Morocco, when the Moroccan navy blocked a harbour to prevent the group's ship from docking.
How has the NGO responded?
They said their ship was being "detained" illegally by Guatemala's military, which it accused of "obstructing a lawful protest against the state's restrictions on the Guatemalan women's right to safe abortion."
The group also urged the Guatemalan government to "remove abortion from the penal code," terming it "a regular medical procedure and a human right". It called for free access to contraceptives and safe abortions.
"Guatemala has been chosen because the laws are very restrictive on the subject of abortion," said Quetzali Cerezo, director of Women in Equity in Guatemala, which assists the Dutch group.