Ahmed al-Kurd, the Hamas government's social affairs minister, confirmed that the aid had been seized.
He said it should be distributed to a wider section of the Gaza population and not only those who hold refugee status and benefit from Unrwa assistance.
UNRWA was set up in 1948 to provide assistance to Palestinian refugees.
It defines Palestinian refugees as those who lost their homes and their means of livelihood as the result of the Arab-Israeli conflict that broke out immediately after the creation of the state of Israel in 1948, as well as their descendents.
The Hamas government "is the main party responsible for the distribution and supervision of this aid in an equitable manner. We reject any discriminatory distinction", he said.
Al-Kurd said Unrwa had given some of its aid to non-governmental organisations with a political agenda, alleging the agency lacked "neutrality and transparency".
Humanitarian assistance is essential in the Gaza Strip, where more than 4,000 homes were destroyed and 20,000 buildings damaged during Israel's 22-day assault.
UNRWA says it is giving food assistance to 900,000 people, out of Gaza's 1.5-million population.
Last week, John Ging, UNRWA's Gaza director, said the agency had expanded its aid programme to include employees of the Palestinian Authority, headed by Mahmoud Abbas, the Palestinian president and leader of Fatah.
Fatah and Hamas are political rivals.
Ging said they needed the aid because Israel was preventing the transfer of cash to the Gaza Strip to pay Palestinian Authority workers.
The overseeing of aid and reconstruction in the Gaza Strip is a source of friction between Hamas and Fatah, which lost control of the territory to Hamas in 2007.
In another development, Salah al-Bardawil, a member the Hamas delegation in Cairo, told Al Jazeera on Wednesday that talks were held in a cordial atmosphere between his side and Egyptian mediators on such issues as a Hamas-Israel ceasefire, Gaza reconstruction and Palestinian national reconciliation.
He said, however, that there are still several unresolved issues, namely guarantees from Israel on its commitment to implement the terms of any ceasefire agreement; the mechanism of opening the Gaza crossings and commitment to the agreed deadline; and guarantees to lift the siege and to not obstruct the entry of reconstruction material to Gaza by Israel.
Al-Bardawil could not say that an agreement would be signed on Thursday, but expressed confidence that such a deal would be reached to within days.
He further said that Egypt would host all Palestinian factions, including Hamas, for a conference on February 22 to deal with such issues as national unity, security and political prisoners.