Secretary of State Condoleezza Rice (search) sharply criticized Syria (search) on Monday for what she called unwillingness to close its borders to terrorists she said are to blame for some of the violence in Iraq.

"Their unwillingness to deal with the crossings of their border into Iraq is frustrating the will of the Iraqi people," and leading to the deaths of innocent Iraqis, Rice said en route home from a surprise trip to see Iraq's new leaders.

She said the United States will try to enlist Syria's Arab neighbors to pressure Syria to clamp down.

"We're going to go back and look again at what the neighbors can do to get the Syrians to stop support for these foreign terrorists who we believe are gathering on Syrian territory and coming across," Rice told reporters traveling with her.

The United States has long accused the Damascus government of exporting terrorism.

Rice's 11-hour visit Sunday coincided with the end of a weeklong U.S. Marine campaign to root out followers of Abu Musab al-Zarqawi (search), Iraq's most-wanted militant, along the Iraq side of the border.

Rice also said she is confident Iraq's new multiethnic government can meet important deadlines and will find ways to expand political participation by the Sunni Arab minority.

"They're really struggling with some pretty difficult issues but I thought there was a kind of willingness and even desire to try and broaden the basis of the people who would be involved in writing the constitution," Rice said.

In her comments to reporters on her plane, Rice also touched on several other issues:

— North Korea: Rice warned North Korea (search) against testing nuclear weapons, saying, "Escalation on the part of the North Koreans is going to deepen their isolation a lot." She did not specify what that meant.

She also said she believes South Korea would raise the issue of the North's nuclear program in newly resumed talks between the two Koreas, saying the South considers the nuclear issue "a barrier also to stronger ties with the North."

— Uzbekistan: Rice said the United States was "still trying to understand" what happened in the eastern city of Andijan, where clashes between protesters and security forces left several hundred people dead.

"The main preoccupations are now to encourage everybody to forgo any further violence, to help with the refugees that went into Kyrgystan out of Uzbekistan (search), and to try to deal with the consequences right now of this set of issues," she said.

— Middle East: Rice said Syria was "frustrating" efforts by Palestinian leader Mahmoud Abbas to find peace with Israel. She said Syria has withdrawn its troops from neighboring Lebanon but not its security forces, and said she believes Syria will try to influence upcoming Lebanese elections.

The three-month pause between Iraq's elections and the announcement of a Cabinet sapped some of the momentum from the January referendum and may have emboldened insurgents.

The constitution, due Aug. 15, is the first critical test for the government that took effect last month. It is not clear whether the document will emphasize secular rule or have an Islamic flavor, and how large a role the Sunnis will play in writing it. Also unanswered is the degree of independence the document will afford to Iraq's powerful Kurdish minority.

The constitution is being drafted by a 55-member committee of legislators, most of them from the Shiite majority who dominate Iraq's first democratically elected government.

"If there is to be a united Iraq in the future, then Sunnis have to be included in the processes going forward and just as they've been included in this government," Rice said Sunday. "The drafting of the constitution, which is the next step, will need to have a sense of inclusiveness too."

In stops in the Kurdish region and in Baghdad, Rice tried to nudge Iraq's factions to work together and said the United States remains committed to helping Iraq get on its feet. The United States will co-sponsor a donor conference next month with the European Union, she said.

A surge of militant attacks has killed at least 430 people across Iraq since April 28, when the country's first democratically elected government was announced.

Rice's visit coincided with the grisly discovery of the bodies of more than 30 men, including 10 Iraqi soldiers, who were found shot execution-style in three separate areas of the country.

U.S. military officials have urged Iraqi Prime Minister Ibrahim al-Jaafari to act quickly to avoid a loss of confidence and good will among Iraqis.

More than two years after Saddam's fall, 85 percent of Iraqis complain of frequent power outages, only 54 percent have access to clean water and nearly one-fourth of Iraqi children suffer from chronic malnutrition, a United Nations and Iraqi survey said last week.