BAGHDAD, Iraq — President Bush, seeking to bolster support for Iraq's burgeoning government and U.S. war policy at home, made a surprise visit to Iraq today to meet newly named Prime Minister Nouri al-Maliki and discuss the next steps in the troubled, three-year-old war.

It was a dramatic move by Bush, traveling to violence-rattled Baghdad less than a week after the death of terror chief Abu Musab al-Zarqawi in a bombing attack. He was expected to be in Baghdad a little more than five hours.

Bush met with al-Maliki in the heavily fortified green zone at a palace once used by Saddam Hussein. It now serves temporarily as the U.S. Embassy.

"Good to see you," exclaimed al-Maliki, who didn't know Bush was in Baghdad until five minutes before they met.

"Thanks for having me," Bush said. They smiled broadly and gave each other a two-handed handshake in the high-domed marble room.

The trip was known only to a handful of aides and a small number of reporters sworn to secrecy because of obvious security threats for Bush and members of his entourage.

The prime minister had been invited to the embassy on the pretense of taking part in a video conference with Bush, supposedly at Camp David, the presidential retreat in Maryland's Catoctin Mountains.

Aside from al-Maliki and his cabinet, Bush was to see Jalal Talabani, Iraq's largely ceremonial president. Bush also was to meet with the speaker of the parliament, national political leaders and U.S. troops.