SDE BOKER, Israel, (Reuters) – Israel is ready to release many jailed Palestinians in return for a soldier seized by militants in June, Israeli Prime Minister Ehud Olmert announced on Monday, saying he was reaching out for peace.

In a major policy speech, Olmert offered to ease travel restrictions on Palestinians and free up frozen funds if violence against Israel ended. He repeated his readiness to give up some occupied land for an eventual peace agreement. “We are ready and willing to pursue this path, and persevere until we reach the sought-after solution,” Olmert said.

Within hours of Olmert’s address, Palestinian militants in Gaza fired rockets into the Israeli border town of Sderot, despite a ceasefire declared on Sunday. Nobody was hurt.

Al-Aqsa Martyrs Brigades, part of Palestinian President Mahmoud Abbas’s Fatah faction, claimed responsibility for the attack, which followed the killing of two Palestinians in an Israeli raid in the West Bank, where a truce is not in effect. “In response to the prime minister extending his hand in peace, we see what some Palestinian factions are giving in return,” Olmert spokeswoman Miri Eisin said.

Apart from a few salvoes just after the ceasefire began on Sunday, militants have largely refrained from firing rockets.

Both Olmert and Abbas are under growing U.S. pressure to show progress on ending decades of conflict. Sudden new talk of peacemaking comes days before visits to the region by President George W. Bush and U.S. Secretary of State Condoleezza Rice.

If the truce lasts, it could ease domestic pressure on Olmert after an inconclusive war with Hezbollah guerrillas.

In his speech, Olmert repeated that he was willing to dismantle many settlements Israel has built in the West Bank, which it captured in the 1967 war, to get “real peace”.

Olmert did not give details or mention a unilateral “realignment plan” shelved after the recent Lebanon war. “With Gilad Shalit’s release and his return safe and sound to his family, the Israeli government will be willing to release many Palestinian prisoners, even those who have been sentenced to lengthy terms,” Olmert said.

It was the first time he had offered to exchange prisoners for Shalit, whose capture in a cross-border raid by Palestinian militants triggered an Israeli offensive into the Gaza Strip.

The governing Hamas movement said Olmert’s offer “was not enough”, alluding to its demand for a simultaneous exchange of more than 1,000 Palestinian prisoners for Shalit. The Islamist militant group called Olmert’s proposal a retreat. The Gaza truce, designed to halt rocket attacks and an Israeli offensive, is seen as a step to reviving talks that collapsed in 2000 before a Palestinian uprising broke out. But Olmert listed a string of conditions for peace talks with Abbas. He said Palestinians must first form a unity government that met Western demands to recognise Israel, renounce violence and accept existing interim peace accords, and Shalit must be freed.

Peace hopes have dimmed since Hamas came to power in March. It is engaged in so far unsuccessful talks with Abbas on a coalition of technocrats that Palestinians hope can lead to an easing of Western sanctions. Commenting on Olmert’s speech, senior Hamas legislator Mushir al-Masri said the group would continue to reject “conditions that contradict the rights of our people”.

Nabil Abu Rdainah, an Abbas adviser, called for a return to peace negotiations. The European Union hailed Olmert’s speech and the ceasefire as signs of hope. The United States has also welcomed the truce. Bush is due to arrive in Jordan on Wednesday for a summit with Iraqi Prime Minister Nuri al-Maliki. It is possible Abbas and Bush would meet there, an aide to the Palestinian president said. Rice is also in the Middle East this week.