Baghdad, Iraq ? Carried out with all the stealth and swagger of a military mission, a surprise visit to Baghdad by President Bush on Tuesday was intended to catch two waves of success: formation of a tough new government in Iraq and the killing of a reviled insurgent leader.

For the moment, at least, Bush appeared to be riding those waves with a gradual improvement in the public’s opinion of the president’s performance in the past month and an additional slight uptick since last week’s killing of insurgent leader Abu Musab al-Zarqawi in Iraq.

Following unremitting bad news from Iraq that dragged Bush’s approval ratings to an all-time low this spring, the president has caught a few breaks that could offer his administration hope.

The convergence of positive signs for an embattled president Tuesday included word that his chief political adviser, Karl Rove, would not be indicted in an investigation of who leaked the identity of a CIA agent.

Bush’s appearance in Baghdad’s fortified Green Zone on Tuesday – which came as a surprise even to Iraqi Prime Minister Nouri al-Maliki – marked the first grand statement the president has attempted to make about the prospects for success in Iraq since he spent Thanksgiving with American troops in Baghdad in 2003.

President Bush, center, gestures during a teleconference with members of the U.S. And Iraqi cabinet members Tuesday at the U.S. Embassy in Baghdad, Iraq. From left are U.S. Ambassador to Iraq Zalmay Khalilzad, Bush, Iraqi Prime Minister Nouri al-Maliki and Iraqi President Jalal Talabahi.

“My message to the Iraqi people is this: Seize the moment,” Bush told U.S. troops assembled for a brief but spirited address by the commander in chief on his way out of Baghdad. “I also have a message to the Iraqi people that when America gives a commitment, America will keep its commitment.”

That steadfastness in Iraq has injured Bush politically as public support for the war has fallen dramatically since the U.S.-led invasion in March 2003. Even now, with public support for the president’s performance showing signs of rebounding somewhat in recent weeks, opposition to the war remains entrenched.

Public approval of Bush’s performance climbed to 38 percent in a new Gallup Poll taken June 9-11, after the U.S. raid that killed al-Zarqawi, the most wanted man in Iraq. That is only a marginal gain from the 36 percent approval recorded before the raid, but a notable boost from 31 percent in early May, the low point in Gallup’s polling of Bush’s presidency.

Nevertheless, because of lingering public opposition to a costly war in its fourth year, analysts suggest that the president and his party could be riding only a passing wave of success. The same Gallup survey shows Americans more likely to support Democrats than Republicans in November’s midterm elections.

The president’s appearance in Baghdad, unannounced to the Iraqi prime minister until just minutes before Bush’s arrival out of concern for the president’s security, risked undermining the Iraqi leader’s stature as head of a sovereign nation, analysts said. It made “kind of a sad statement” about the U.S.-Iraqi relationship, according to Peter Singer, a senior fellow in foreign policy at the Brookings Institution.

“As for the Iraqi public, they couldn’t care less” about the Bush appearance with al-Maliki, said Singer, director of Brookings’ Project on U.S. Relations with the Islamic World. “They are more concerned about what life is like from day to day for them. … They are worried about the massive crime wave and whether their children are safe on the streets, not whether Bush showed up or not.”

Any political benefits of the Baghdad visit for Bush back home also could be undone if the war continues to go badly.

“Theater sometimes works politically,” said John Mueller, a professor of political science at Ohio State University who has tracked declining public support for wars as casualties increase. “If it has a positive impact for him, it will be extremely temporary. The reality is that the war is a mess, the killings continue and the insurgency continues.”