UNRWA, the UN agency in charge of Palestinian refugees, denies the allegation.
COGAT, the defence ministry agency responsible for civilian affairs in the Palestinian territories, says that Sohail al-Hindi was appointed to the militant group's leadership in a February 13 internal election.
"Amongst other members elected to the political bureau, al-Hindi was also appointed as a senior Hamas member from Jabalia in northern Gaza," it said in an English-language statement.
"He also holds positions as both the Chairman of the Association of Palestinian Workers of UNRWA since 2012 and as an elementary school principal in the Gaza Strip," it added.
More From This Section
The Israeli foreign ministry made the same allegation on Thursday on its official Twitter account.
UNRWA issued a denial the next day.
"As soon as the allegations came to UNRWA's attention, the Agency undertook a preliminary investigation, including discussing the allegations with the staff member," it wrote.
"Based on the due diligence carried out by the agency to date, UNRWA has neither uncovered nor received evidence to contradict the staff member's denial that he was elected to political office."
It said that agency staff are regularly advised that political activity or fundraising is considered improper conduct.
"If any new allegations come to light, we will look into them immediately and thoroughly," it added.