RAMALLAH, West Bank, June 29 (Reuters) - Discontent with Hamas over slow-moving Palestinian unity talks and Israel's ban on Gaza reconstruction aid have led to a sharp decline in the Islamist group's popularity, an opinion poll showed on Monday.

The survey by the Jerusalem Media and Communications Centre (JMCC) put public support for Hamas in the West Bank and Gaza Strip at 18.8 percent compared with 27.7 percent in its previous poll in January.

Palestinian President Mahmoud Abbas's Fatah faction is now more popular than Hamas with a 34.9 percent rating, up from 26 percent in January, according to the poll of 1,199 people.

Khader Khader, head of the media unit at the East Jerusalem-based JMCC, said Hamas's popularity was hit by discontent in the Gaza Strip, where the group rules, over a lack of movement in Egyptian-sponsored unity talks with Fatah and in reopening the territory's borders.

According to the poll, 26.5 percent of those surveyed blamed Israel for the deadlock in the Hamas-Fatah dialogue while 23.5 percent pointed a finger at Hamas and 15.5 percent said Fatah was responsible. It's a sort of protest by the people (of Gaza) because there is no progress on these two major issues, Khader said.

Some 5,000 Palestinian homes were destroyed during the 22-day offensive that Israel launched in the Gaza Strip last December with the declared aim of curtailing cross-border rocket attacks by militants.

Despite international calls to ease hardship in the Gaza Strip, Israel has barred reconstruction material from entering the territory because it said the material could be used by Hamas to make weapons.

Israel tightened restrictions at its border with the Gaza Strip after Hamas took control of the enclave in 2007 after defeating Fatah forces.

Israeli officials said the frontier could begin to reopen if an Israeli soldier, held by militants in the Gaza Strip for the past three years, was released. Hamas is demanding Israel free hundreds of Palestinian prisoners in return for the soldier. (Writing by Mohammed Assadi; Editing by Robert Woodward)