New Zealand chaired the Al-Qaeda Sanctions Committee, which was tasked with counter-terrorism measures including targeted sanctions for terrorist groups.
"We are in that sense directly involved in the Security Council mechanism that monitors sanctions and seeks to impose the controls [on] ISIL," Mr van Bohemen said.
The Security Council has passed a resolution which banned the trade of oil, stolen antiquities and other goods with ISIS.
If any entities were found to be purchasing from ISIL, the UN could order sanctions against them.
Mr van Bohemen said he understood that ISIL's income flow was beginning to dry up.
"As you know, it is an area of lawlessness, particularly around Syria. There is no national police force around Raqqa and places like that.
"But I am confident that the pressure is going on. These sanctions regimes work through a process of slow strangulation rather than overnight impact."
Mr van Bohemen said that while the council's membership was divided around how to deal with the Syrian conflict, member nations were unified in taking action against ISIL.
In its first month on the council, New Zealand also made its position clear on the Israel-Palestine situation.
Mr van Bohemen said: "We deliberately cast our statement at the level of general principle. We wanted to make it clear that we support the two-state solution, that we want an end to the occupation, we want two governments living in peace and we want the council to have a role in advancing that outcome."
He said the statement was seen as "quite a strong position" by council members.
A motion tabled by Jordan to establish an independent Palestinian state and end Israeli occupation fell short by one vote late last year.
A similar motion was expected to be reintroduced this year.