Hamas has said the seizure was a mistake and that they are working to return the lorries.
According to UNRWA, it was the second time this week that Hamas members had seized aid supplies.
Its officials said that Hamas members had seized 3,500 blankets and 400 food parcels at gunpoint from an UNRWA store on Tuesday.
Mike Kirsch, Al Jazeera's correspondent reporting from Gaza City, said: "Hamas officials are saying this whole thing is just a big misunderstanding.
"They are saying that the 10 trucks that were intercepted ... they believed was aid coming from Hamas, from the ministry of social affairs, that was on the Israeli border, in effect that the trucks got mixed up with the UN trucks.
"And what has since happened is that Hamas has received documentation from the UN that verifies that these trucks belonged to the UN and Hamas is now saying these trucks will be returned on Saturday."
Christopher Gunness, a UNRWA spokesman, told Al Jazeera that UN aid shipments into Gaza will not restart until all the aid seized by Hamas is returned.
"Until we get all of this aid back, and until we receive credible assurances from the Hamas government, the suspension of our imports of aid into Gaza will continue," he said.
"Let me make one thing clear, we have some supplies in Gaza, we are going to continue with those distributions those are not suspended."
Gaza is in the midst of a humanitarian crisis. A stiffling economic blockade imposed by Israel for the past 18 months has crippled its economy and caused severe food and medicine shortages.
Israel's 22-day long assault on the Palestinian territory has worsened the situation further, forcing many Palestinians to live on handouts.
Speaking to Al Jazeera, Ahmed Yousef, a senior Hamas offical, said: "Our relationship with UNRWA is a strategic one. There are some mistakes that have been committed by some people."
He said steps were being taken to resolve the issue.
A senior Hamas leader, however, had earlier in the week accused UNRWA of indulging in discrimination in its distribution of aid.
Ahmed al-Kurd, the Hamas government's social affairs minister in Gaza, had demanded that aid be distributed more "widely and fairly".
UNRWA only provides assistance to those Palestinians holding refugee status.