Marlin told a press conference in the island's capital Philipsburg he was quitting, Dutch media reports said.
"He (Williams) said he will send his resignation letter to the governor later," Dutch public broadcaster NOS said.
Williams will be replaced by his deputy and justice minister Rafael Boasman, NOS added.
Dutch Prime Minister Mark Rutte earlier today demanded Williams' resignation after he refused to step down despite two votes of no confidence by lawmakers in St Martin's parliament.
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Marlin has twice faced votes of no-confidence this month after he refused to accept conditions set by The Hague for releasing some 550 million euros (USD 653 million) in aid to the island, hit hard by Hurricane Irma more than two months ago.
A war of words broke out when the Caribbean leader in October refused to agree to conditions for aid, including setting up a special "integrity" chamber to oversee the spending and combat possible corruption.
"The Netherlands is ready to help, but everybody has to stick to the democratic rules of the game," he said.
Marlin -- known for his anti-Dutch rhetoric -- in turn accused The Hague of a "political conspiracy" to get him ousted, telling the NOS he was bearing the brunt of the blame "for everything from global warning to a dog barking."
St. Martin, located south of the island of Anguilla, is divided between the Netherlands and France.
Next parliamentary elections on the island are slated for February, but many say it will be difficult to organise them after Irma destroyed 70 percent of the island's infrastructure.