"We intend to help remove all obstacles in the way of pilgrims and we do not object to those who have been registered in Ramallah leaving the Gaza Strip," Gaza's de-facto Prime Minister Ismail Haniyeh said.
Radio reports quoted eyewitnesses as saying earlier in the day that police in Gaza had cordoned off roads to the Egyptian border and were seizing travel documents issued by the Saudis through the Palestinian National Authority.
The Palestinian National Authority controls the West Bank and does not recognize Hamas as the legitimate ruler of the Gaza Strip.
A spokesman for the Gaza Interior Ministry, Ihab al-Ghusain, said that residents in Gaza who had applied for hajj documents via Hamas had been turned down by the Saudi authorities.
Egyptian authorities announced on Thursday that they were reopening the Rafah border crossing with Gaza to allow Palestinian hajj pilgrims to make their way to Saudi Arabia and Mecca.
Egypt and Israel closed their border crossings with the Gaza Strip after Hamas seized control of the enclave in June 2007. The blockade has led to a drastic deterioration in the humanitarian situation in Gaza, according to aid agencies working in the region.