"Frankly, a decision to let people that have been vetted for what is perhaps the most prestigious foreign educational programme run by the United States ... it ought to be falling off a log for them to be able to do this."
Israel has tightened its military cordon around the Gaza Strip since the Hamas group took over the territory nearly a year ago and it gives few Palestinians, besides some who are gravely ill, permission to leave.
The Fulbright Student Program brings citizens of other countries to the US for masters degrees or PHD studies at US universities and other institutions.
Abdulrahman Abdullah, one of the seven students, told Al Jazeera the US consulate had told him that it may be easier for him to apply for the programme again next year.
"It was very difficult to get the scholarship. There were many exams and tests and its really difficult to go through this process again."
Hadeel Abu Kawik, a computer and engineering student, said she was surprised that the US was unable to secure her permission to travel.
"I was astonished at how the United States government cannot get a few students out of Gaza."
Arye Mekel, an Israeli foreign ministry spokesman, said a few of the Fulbright students had recently left Gaza through the Erez crossing.
US officials had no comment on this and it was not immediately possible to obtain independent confirmation.
Condoleezza Rice, the US secretary of state, suggested she disapproved of the move to reallocate the money for the seven Gaza students who hope to pursue advanced degrees at American institutions this autumn.
"I can tell you it was a surprise to me," Rice said at a news conference while on a visit to Iceland.
"I am a huge supporter of Fulbrights."
Despite the blockade, about 500 students and their dependents managed to get out of Gaza over the past year with the help of Israeli permits, according to Gisha, a group that works for freedom of movement for Palestinians.
But restrictions were tightened late last year in what Israel says is a response to Palestinian attacks, and few student permits have been issued since.