The four men - Rahman Mizanur, Miah Rubel, Jabath Kysar Haje Norul Islam Sowdagar and Sohel Hawlader Ismail Hawlader - pleaded guilty to one and two counts each of providing or collecting hundreds of dollars.
The convicts, employed in the local construction and marine industries, face up to 10 years in jail and are expected to be sentenced on June 21.
Ringleader Mizanur, 31, pleaded guilty to two of four charges against him. The remaining two charges will be taken into consideration during sentencing, according to a 'Channel News Asia' report.
Mizanur had set up the group called Islamic State in Bangladesh, in March this year after developing a "liking" for the dreaded ISIS terror group.
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The court heard that Mizanur had tried to join ISIS three times, but was unable to obtain a visa allowing him to travel to Turkey and Algeria.
He travelled to Singapore to find work instead, and recruited his five co-accused, four of whom pleaded guilty alongside him.
The group met regularly to discuss waging an armed jihad to fight against non-believers.
They agreed that when they returned to Bangladesh, they would "find and kill" non-believers, the prosecution told the court.
In January this year, the four had taken an oath that they would follow Abu Bakar al-Bagdadi, the leader of ISIS, until their deaths, the court heard.
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Daulat, who was the "security council" of the group, said he did not know the money he contributed would be used for terrorism activities.
The men had intended to join Islamic State as foreign fighters, but upon realising it would be difficult to travel to Syria, focused their plans closer to home, Singapore's Ministry of Home Affairs (MHA) had said.
Based on investigations, the group had identified several possible attack targets in Bangladesh, and possessed documents on weapons and bomb-making, as well as ISIS and al Qaeda radical material, it said.
A sixth man - Mamun Leakot Ali, who took over as leader of the group after Mizanur was arrested in March - had denied the charges against him at a hearing last week.
If found guilty of financing terrorism, the men could be jailed up to 10 years, fined up to Singapore dollars 500,000 per charge, or both.
Another two men, Sohag Ibrahim and Islam Shariful, both 24, will be dealt with separately.
They were listed as witnesses in the case this morning against the five men.