JERUSALEM, June 27 (Reuters) - The parents of an Israeli soldier held in the Gaza Strip since 2006 began a 12-day march on Sunday from their northern home to Prime Minister Benjamin Netanyahu's Jerusalem residence to press for a prisoner swap.

We are strong enough to (trade) hundreds of murderers for Gilad Shalit, said Shimshon Liebman, head of the public campaign for the soldier's release. Then, I am sure that every soldier will know that we are not leaving them behind.

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

Israel and Hamas Islamists who now run the enclave have failed to agree terms of a swap in which around 1,000 of the 7,000 Palestinian prisoners held in Israeli jails would be released in exchange for Shalit.

Netanyahu has balked at allowing Palestinians convicted of killing Israelis to go free in West Bank areas where they could launch further attacks.

Hamas had accepted that some prisoners would be exiled but wanted to be able to choose their destinations, said sources familiar with the German-mediated negotiations.

Thousands of Israelis were expected to join Shalit's parents and relatives on the trek from northern Israel to Jerusalem.

Stepping up pressure on Netanyahu to agree to a deal, Shalit's family said it would camp indefinitely outside his official residence on July 8, two days after the Israeli leader is due to meet U.S. President Barack Obama in Washington.

Netanyahu told reporters he would invite Shalit's parents to meet him when he returns from his U.S. visit.

I want to see you. I will happy to meet you. This won't be our first meeting ... Our heart goes out to Gilad and his family, Netanyahu said, appealing to the international community to press Hamas to release the soldier. (Writing by Jeffrey Heller; Editing by Peter Graff)