By Nidal al-Mughrabi

GAZA (Reuters) - Egypt opened the Rafah border crossing on Wednesday for the first time in a month to allow thousands of stranded Palestinians to return to the Gaza Strip, border officials said.

However, the frontier remained closed in the other direction, making it impossible for the vast majority of Gazans to leave the densely populated Mediterranean enclave.

The Rafah crossing was shut on Oct. 25 after Islamist militants in Egypt's adjacent Sinai region killed 33 members of the security forces in some of the worst anti-state violence since Islamist president Mohamed Mursi was toppled in July 2013.

The month-long closure marooned around 6,000 Palestinians in Egypt and third countries, while around a thousand people in Gaza are desperate to get out for medical treatment inEgypt, officials in Islamist-ruled Gaza say.

Egyptian state television said outbound traffic would be allowed from 12 p.m. to 4 p.m. (1000-1400 GMT) on Wednesday and from 7 a.m. to 4 p.m. (0500-1400 GMT) on Thursday.

Impatient to return home, hundreds of Palestinians swiftly started to cross as soon as the border offices opened.

"The situation was very difficult. People ran out of money, others were sick, it was tough for everyone. Some went to mosques to sleep because they had no money," said Fadwa Almoghrabi, who was stuck in Cairo for 20 days on her way back from visiting relatives in the Gulf.

Travellers said a combined 11 hours of openings would not be enough to allow the thousands of stranded Gazans to return.

Rafah is the only major border crossing into the impoverished Gaza Strip that does not go through Israel, which also blockades the territory.

Gaza is controlled by the militant Islamist group Hamas, which has long had ties to theMuslim Brotherhood that was ousted from power in Egypt when Mursi was overthrown.Hamas's relations with the current Egyptian government are tense.

Maher Abu Sabha, the Hamas-appointed director of the crossings, urged Egyptian authorities to allow hundreds of Palestinians stranded in third countries to fly to Egypt so they could immediately travel to the border and enter Gaza.

Hamas leaders have repeatedly distanced themselves from violence in Egypt and in Sinai and say they have no armed presence in areas outside Palestinian boundaries.

Following the attacks last month, Egypt stepped up military operations in Sinai and razed homes to create a kilometre-wide buffer zone abutting Gaza.

It aims to destroy a network of tunnels that have funnelled weapons into Gaza, and that are also used to import consumer goods that provide vital income to the isolated territory.

A devastating 50-day war between Hamas and Israel in July and August levelled entire neighbourhoods of Gaza and left thousands of people homeless. Much reconstruction aid is arriving via the Israeli-controlled border points.

(Reporting By Yusri Mohamed in Ismailia, Mahmoud Mourad in Cairo and Nidal Al Mughrabi in Gaza; Writing by Shadi Bushra; Editing by Lin Noueihed, Mark Heinrich and Crispian Balmer)