Speaking on Monday, Abdelrahman Abdulla, one of the seven successful applicants, said: "Yesterday I received a letter from US consulate-general in Jerusalem, saying that they are talking with the Israeli government in order to give us exit permits from Gaza, so that we can reach the consulate in Jerusalem.
Mark Regev, spokesman from the Israeli ministry of foreign affairs, told Al Jazeera that he "wasn't aware there was a problem" with this case of the movement of Gaza students.
He said Israel intially received no notification from Fulbright that the students in question were "bonafide".
Regev said that Israel has an "interest in seeing people like this going to study abroad".
"Ultimately, in view of creating a Palestinian leadership composed of individuals exposed to pluralist countries like the US," he said.
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 the statement and it was not immediately possible to obtain independent confirmation.
Right to education
Israel has tightened its military cordon around the Gaza Strip since Hamas took over the territory almost a year ago.
Few Palestinians are allowed to leave the territory, including some who are gravely ill.
Commenting on the scholarships controversy, Abdulla said: "This is all about our right to education.
"It is really unbelievable that those educated people in Palestine could be denied their higher education.
"It was very difficult to get the scholarship. There were many exams and tests and its really difficult to go through this process again."
Abdullah said that "as Palestinians, we are looking forward to the Palestinian state".
"I highly believe that with our efforts, those young Palestinians can plan for their future to contribute to the movement of their country and the Palestinian community as a whole," he said.
"It's our goal in life."
The issue hit the headlines after Abdullah and the six other Gaza students received on Thursday an email saying their grants had been "redirected" by the Fulbright programme, because of Israel's closing of Gaza.
Condoleezza Rice, the US secretary of state, who said she was a "huge supporter of the Fulbrights", suggested she disapproved of the move to reallocate the money for the seven students.
"I can tell you it was a surprise to me," she said while on a visit to Iceland on Friday.
"If you cannot engage young people and give complete horizons to their expectations and their dreams, I don't know that there would be any future for Palestine."