Rosli, who worked as a car washer, "became convinced that ISIS militants were fighting for Islam and that their beheading of "enemies" was religiously permissible," the ministry said, referring to the Islamic State group by another name.
He "was keen to travel to Syria to fight for ISIS," the statement said, adding that he had researched how to travel to the war torn country.
Omar, a waste truck driver, had made preparations with his wife and children to travel to Syria to join the Islamic State group, the statement said.
"He was prepared to die a martyr," it added.
Singaporean officials have repeatedly warned that the city-state, a key U.S. ally in the region, is a prime target for IS militants.
Earlier this month, Indonesian police arrested six suspected militants over a plot to launch a rocket attack on an up-market Singapore waterfront district from the nearby Indonesian island of Batam.
The alleged leader of the group is accused of planning the attack with a leading Indonesian militant, who is believed to be fighting with the IS group in Syria.
Singapore said in July that it had detained a 44-year-old Australia-based Singaporean who allegedly glorified IS and backed the establishment of a caliphate in the city-state.
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