On his second trip to Israel, President Bush will address the issue of settlement building and try to push for progress on a two-state solution to the Israeli-Palestinian conflict.

JERUSALEM � President Bush landed here Wednesday to join the Jewish state in its 60th anniversary gala � part of his drive to propel Israelis and Palestinians toward a landmark peace deal.

But hours after his arrival, a rocket launched by Gaza militants landed on a shopping mall in Ashkelon, Israel’s southernmost city on the Mediterranean coast, injuring more than 30 people and highlighting the challenge facing Mr. Bush as he tries to push forward negotiations on a two-state solution.

Earlier in the day, Israeli military strikes in Gaza killed two Palestinian civilians and three militants, the Associated Press reported, quoting Palestinian medical officials.

The volley of violence follows weeks of international efforts to get Israel and HAMAS, the Islamist group that controls Gaza, to agree to some kind of truce or calm in which both would promise to stop firing at the other for a limited period of time.

But Israeli leaders say they worry that such a temporary time-out will only give HAMAS a period of time to build up its arsenal and prepare for the next round. And HAMAS, for its part, has refused to link this proposed deal to the release of Israeli soldier Gilad Shalit, who HAMAS has held captive in Gaza for almost two years.

Moreover, Islamic Jihad and Popular Resistance Committee � a group that includes militants in HAMAS � took responsibility for Wednesday’s shopping mall strike. Islamic Jihad has shown itself even more reluctant to agree to a period of calm with Israel. Egyptian mediators have for weeks been trying to forge some agreement, so far without clear success. (Editor’s note: For its part, Israel has continued to announce and build new illegal settlements, which most analysts blame for the lack of progress in peace talks.)

Israeli analysts have said in recent weeks that an attack on an Israeli civilian center � particularly a place other than the small and rocket-scarred Sderot � would be a reason for the Israeli army to launch a major military invasion in Gaza. Wednesday’s attack on Ashkelon brought hundreds of people into the streets nearby, many of them demanding a response from the government.

Prime Minister Ehud Olmert hinted Wednesday that Israel might resort to a harsh response. “What happened today is entirely intolerable,” Mr. Olmert said, “and the government of Israel is committed to stopping it, and we will take the necessary steps to do it.”

It is with this minefield in the background that Bush arrives for his second visit this year, one that administration officials insist is not just for the purpose of marking Israel’s 60th birthday but for actual working meetings on core issues. A State Department official said that Bush would raise the issue of Israeli settlement building in the Occupied Territories and would try to push for progress on a two-state solution to the conflict.

At Israeli President Shimon Peres’s garden Wednesday, Bush said, “I suspect if you looked back 60 years ago and tried to guess where Israel would be at that time, it would be hard to be able to project such a prosperous, hopeful land. I doubt people would have been able to see the modern Israel, which is one reason I bring so much optimism to the Middle East, because what happened here is possible everywhere.”

But as Bush spoke at a gala celebration later in the day largely focused on championing the Israeli-American alliance, he poked fun at the number of months he has left in office by noting the number of former heads of state there were in the audience.

“Save a seat in the ex-leaders club,” he said, eliciting a roar of laughter and applause. Later, he continued with some informal words and humor. “Citizens of Israel, I love coming to your country. Fellow Americans, spend freely and behave yourself. Distinguished guests, I really appreciate your being here with one of America’s closest friends.”

But the congratulations Bush is bestowing on Israel are already underlining a sense of imbalance that Palestinians and neighboring Arab countries feel this administration has demonstrated in dealing with the conflict.

Bush will not be meeting any Palestinians leaders at all during the trip to Israel � he will not go to visit the Palestinian Authority in the West Bank. But he will meet with Palestinian leader Mahmoud Abbas at the World Economic Forum, which begins this weekend in Sharm el-Sheikh, Egypt.