JERUSALEM, July 5 (Reuters) - Thousands of Israelis and dozens of Palestinians separately gathered on either side of the Gaza Strip border on Monday demanding a prisoner swap.

On the Israeli side, the parents of Israeli soldier Gilad Shalit, held in the Gaza Strip for four years, were accompanied by thousands calling for his release in exchange for hundreds of Palestinians Israel is holding in its jails.

Shalit, now 23, was captured by Palestinian militants who tunnelled from the Gaza Strip into southern Israel in June 2006.

Israel and Hamas Islamists, which now runs the coastal enclave, have failed to agree terms for a deal in which around 1,000 of the 7,000 Palestinian prisoners held by Israel would be released in exchange for Shalit.

Shalit's parents and their thousands of supporters listened the Israel Philharmonic Orchestra play Mozart, Beethoven and Verdi at a park a few kilometres from the spot where Shalit was taken. It ended with yellow balloons being released skywards.

The concert was organised by private supporters of the Shalit family who have gained increased sympathy from the Israeli public.

We want to think of Gilad Shalit today, who is suffering for four years, without visitation and we want to do something so that visitation will be allowed and that negotiations will be rapider, said the orchestra's Indian conductor Zubin Mehta.

The dozens of Palestinian demonstrators on the Gaza side close to the Erez border crossing held banners that read: Both of us have the same goal and now you have the chance to release your son as well as our sons and daughters.

Shalit's parents began a planned 12-day march on June 27 from their home in northern Israel and have daily been accompanied by thousands along the way to their destination, the Jerusalem residence of Prime Minister Benjamin Netanyahu.

The Israeli leader said last week he was prepared to release 1,000 Palestinian prisoners in exchange for Shalit, but that he could not countenance a deal in which top terrorists would be released and that many would have to be exiled.

The Palestinian demonstrators in Gaza also held a banner telling the Shalits that the main responsibility for the fate of their son lay with the Israeli government.