BAGHDAD, Iraq -- Suicide bombers and gunmen killed nearly two dozen people across Iraq on Sunday, shattering the relative quiet since the parliament election, as President Bush said the vote had strengthened a new ally and warned against a U.S. pullout.

Hours before Bush spoke, Vice President Dick Cheney made a surprise visit to Iraq and said the election's strong turnout had brought Iraq closer to taking control of its own security. But Cheney also cautioned against a rapid U.S. withdrawal.

Germany's government, meanwhile, said kidnappers had freed a German woman who was taken hostage in northern Iraq more than three weeks ago. Susanne Osthoff, a 43-year-old aid worker and archaeologist, was reported in good condition at the German Embassy in Baghdad.

A series of attacks that began late Saturday ended three days of near calm that began with Thursday's elections for the first full-term parliament since Saddam Hussein was toppled.

Most of the people killed in the new violence, which included two suicide bombings, were police officers. The bloodshed came after authorities eased security measures ordered for the elections and traffic returned to normal on the first full working day since the vote.

Cheney's visit was so secret that Iraqi Prime Minister Ibrahim al-Jaafari was surprised when he met him at the U.S. ambassador's residence in the heavily fortified Green Zone.

The one-day trip focused on the successful legislative election and the strong turnout in all of Iraq's religious and ethnic communities.

"The participation levels all across the country were remarkable," Cheney told reporters after an hourlong briefing from U.S. military commanders. "And that's exactly what needs to happen as you build a political structure in a self-governing Iraq that can unify the various segments of the population and ultimately take over responsibility for their own security."

The big turnout -- particularly among Sunni Arabs who boycotted the election of an interim legislature last Jan. 30 -- has raised expectations that increased political participation may undermine the Sunni-led insurgency and allow U.S. troops to begin pulling out next year.

But Cheney stressed the Bush administration did not plan a rapid withdrawal.

"You've heard some prominent voices advocating a sudden withdrawal of our forces from Iraq," he told hundreds of troops. "Some have suggested that the war is not winnable, and a few seem almost eager to conclude the struggle is already over. But they are wrong. The only way to lose this fight is to quit, and that is not an option."

Al-Jaafari told Cheney that he estimated a record 70 percent of Iraq's 15 million registered voters went to the polls.

"We have been able to move forward several decades. The year 2005 is the most important in the history of Iraq in terms of productivity, of the establishment of the democratic process, the establishment of the constitution, the establishment of the Iraqi parliament," he said.

Iraqi authorities were still tallying the ballots that will determine the allocation of the parliament's 275 seats for four-year terms.

The election commission said it had received raw preliminary results from seven provinces representing about 70 percent of the total vote. Official Safwat Rashid said that they included Baghdad, Babil, Karbala, Najaf and Irbil, Anbar and Kirkuk and that the rest were "on their way."

He added that on Monday "we'll be able to provide you with 80 percent of the results for Baghdad province. The rest will be completed in the coming days."

Rashid said the commission had so far received 345 complaints about the election, more than half claiming violations of campaigning rules. Other complaints were about names missing from voter rolls and some alleged interference with voters by party officials, police or elections workers.

The commission began examining complaints Sunday. "Some of the complaints are minor and others may be grave enough to cancel the results of a ballot box," Rashid said.

The complaints have to be dealt with before election results are released, a process that officials have said would take about 10 days.

Shiite Arabs account for about 60 percent of Iraq's estimated 27 million people, compared with 20 percent for Sunni Arabs and a similar proportion for Kurds. Shiite and Sunni political leaders have said they likely will have to form a coalition Cabinet to govern.

At least one hardline Sunni Arab politician, Saleh al-Mutlaq, said Sunday that the turnout was a sign that insurgents are ready to participate in the political process.

"By abiding to its promise not to attack the voting process, the resistance has proved that it is ready to lay down its arms if the dialogue and democratic process is genuine," said al-Mutlaq, who heads the Iraqi Front for National Dialogue.

In Berlin, German Foreign Minister Frank-Walter Steinmeier offered no details in announcing the release of aid worker Susanne Osthoff, saying only that she was free and now at his country's embassy.

Osthoff, 43, and her Iraqi driver disappeared Nov. 25 in northern Iraq. Days later, the two were shown in a videotape blindfolded and sitting on a floor, with militants -- one armed with a rocket-propelled grenade -- standing beside them.

The captors threatened to kill the hostages unless Germany stopped dealing with the Iraqi government. German Chancellor Angela Merkel responded that her country would not be "blackmailed."

While Germany strongly opposed the U.S.-led invasion of Iraq and refused to send troops here, it does train Iraqi soldiers and police outside this country.

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Associated Press reporter Nedra Pickler in Baghdad and Pete Yost in Washington contributed to this report.