PHONM PENH, Cambodia — The Middle East once again reordered administration priorities as President Barack Obama’s intent to reassert U.S. influence in Asia was overshadowed by an escalating conflict between Israel and the Palestinians.

Obama’s three-day Asia trip, his first since winning re-election, included historic visits to Burma and Cambodia and a summit of Southeast Asian leaders.

Yet his most urgent conversations were those he had by telephone with Egyptian President Mohammed Morsi and Israeli Prime Minister Benjamin Netanyahu as rocket attacks on Israel by Palestinian militants and the Jewish nation’s response threatened to spiral into further violence.

“The Middle East has a way of derailing other presidential foreign-policy agendas and forcing its way onto the world stage,” said Daniel Byman, a professor in the School of Foreign Service at Georgetown University in Washington. “Other recent presidents have tried to downplay the Middle East, but all found themselves heavily involved one way or another despite their efforts.”

As he has wound down the wars in Iraq and Afghanistan, Obama has made explicit his goal to shift U.S. focus to the Asia-Pacific region, which accounted for 60 percent, or $895 billion worth, of total U.S. goods exports. The outreach is spurred by the rising commercial importance of Pacific Rim nations as well as the expanding military and economic power of China, the world’s biggest economy after the U.S.

While Obama’s public schedule kept to the agenda of trade and encouraging the expansion of economic and political freedom, behind the scenes the Middle East was at the forefront.

Moments after he visited Burma’s opposition leader Aung San Suu Kyi on Monday, Obama met with Secretary of State Hillary Rodham Clinton and national security adviser Tom Donilon at the U.S. Embassy in Burma for a briefing on the fighting between Israel and Palestinians in the Gaza Strip.

Throughout the trip, Obama, Clinton and Donilon were in contact with their counterparts in other capitals.

After arriving in Phnom Penh, Cambodia, and meeting with leaders of the Association of Southeast Asian Nations, Obama called Morsi late Monday to press him on getting Hamas to stop firing rockets into Israel. Within 24 hours he spoke with the Egyptian leader twice more, including aboard Air Force One as he began the flight back to the U.S.

The fighting also is a crucial test of whether the U.S. can count on Morsi to uphold Egypt’s alliance with the U.S.

In their last phone conversation, Obama commended Morsi for “his efforts at de-escalation,” Ben Rhodes, Obama’s deputy national-security adviser, told reporters traveling with the president. While the U.S. views Morsi as “sincere” in his desire to quell the conflict, “We also understand that Gaza is an extraordinary challenge,” Rhodes said.

Obama also spoke with Netanyahu, and the White House repeated statements of support for Israel’s right to defend itself and setting the blame for the conflict on Hamas firing rockets at Israeli cities.

Hours before leaving Cambodia, his final stop, Obama dispatched Clinton on an emergency mission to the Mideast with stops in Jerusalem, Ramallah and Cairo.

Separately, the U.S. Navy’s 6th Fleet commander in Europe is extending deployment in the Eastern Mediterranean of the 4,000-person 24th Marine Expeditionary Unit and its three amphibious warfare vessels just as it was transiting the region on the way to the U.S., said Lt. Cmdr. Chris Servello, a Navy spokesman.

The decision is a “prudent measure allowing” the unit “to be positioned for any contingency,” Servello said in a telephone interview. The unit will stay in the area “until further notice,” Servello said.

Jonathan Pollack, an Asia expert at the John L. Thornton China Center at the Brookings Institution in Washington, said Clinton’s decision to leave the Asian summit to address the Gaza crisis underscores the difficulty in promising a “pivot” or “rebalance” of forces toward the Pacific.

“This shows you the absolute liability of defining a strategy by a bumper sticker,” Pollack said. “There is no easy escape or exit from the Middle East.”

Over the long term, Asia is more central to U.S. policy, according to Michael Mandelbaum, a professor at Johns Hopkins University’s School of Advanced International Studies in Washington.

“That’s where the economic growth is going to come from,” Mandelbaum said. “That’s where the danger of a truly disastrous war looms, one that could involve China.”

The diversion of the president’s attention from Asia to the Middle East is “a case of the urgent driving out the important,” he said.

Information for this article was contributed by Daniel Ten Kate, Tony Jordan, Laura Litvan, David Lerman, Tony Capaccio and Mark Shenk of Bloomberg News.

Front Section, Pages 7 on 11/21/2012