DAMASCUS, Syria (AP) - House Speaker Nancy Pelosi mingled with Syrians in a market and made the sign of the cross at a Christian tomb Tuesday in a visit to hard-line Syria that was criticized by President Bush. Bush said the visit sends mixed signals to Syria's government, which his administration accuses of supporting terrorism. The United States says Syria allows Iraqi Sunni insurgents to operate from its territory, backs the Hezbollah and Hamas militant groups and is trying to destabilize the Lebanese government. Syria denies the allegations. Pelosi's visit to Syria was the latest challenge to the White House by congressional Democrats, who are taking a more assertive role in influencing policy in the Middle East and the Iraq war. The Bush administration has resisted calls for direct talks to help ease the crisis in Iraq and make progress in the Israel-Palestinian peace process. Soon after Pelosi's arrival in Damascus, Bush criticized her visit. "A lot of people have gone to see President Assad ... and yet we haven't seen action. He hasn't responded," he told reporters at a Rose Garden news conference. "Sending delegations doesn't work. It's simply been counterproductive." Pelosi, a California Democrat, did not comment on Bush's remarks before heading from the airport to Damascus' historic Old City. She was scheduled to meet President Bashar Assad on Wednesday. Wearing a flowered head scarf and a black abaya robe, Pelosi visited the 8th-century Omayyad Mosque, shaking hands with Syrian women inside and watching men in a religion class sitting cross-legged on the floor. She stopped at an elaborate tomb, said to contain the head of John the Baptist, and made the sign of the cross. About 10 percent of Syria's 18 million people are Christian. At the nearby outdoor Bazouriyeh market, Syrians crowded around, offering her dried figs and nuts and chatting with her. She strolled past shops selling olive oil soaps, spices and herbs, and at one point bought some coconut sweets and eyed jewelry and carpets. Democrats have argued that the U.S. should engage its top rivals in the Mideast - Iran and Syria - to make headway in easing crises in Iraq, Lebanon and the Israeli-Arab peace process. Last year, the bipartisan Iraq Study Group recommended talks with the two countries. Bush rejected the recommendations. But in February, the U.S. joined a gathering of regional diplomats in Baghdad that included Iran and Syria for talks on Iraq. Visiting neighboring Lebanon on Monday, Pelosi shrugged off White House criticism of her trip to Syria, noting that Republican lawmakers met Assad on Sunday without comment from the Bush administration. "I think that it was an excellent idea for them to go," she said. "And I think it's an excellent idea for us to go as well." She said she hoped to rebuild lost confidence between Washington and Damascus and will tell Syrian leaders that Israel will talk peace with them only if Syria stops supporting Palestinian militants. She has said she will also talk to the Syrians about Iraq, their role in Lebanon and their support for the Hezbollah militant group. "We have no illusions but we have great hope," said Pelosi, who met with Palestinian President Mahmoud Abbas in the West Bank city of Ramallah earlier Tuesday. Relations between the U.S. and Syria reached a low point in early 2005 when Washington withdrew its ambassador to Damascus to protest the assassination of former Lebanese Prime Minister Rafik Hariri. Many Lebanese blamed Syria - which had troops in Lebanon at the time - for the assassination. Damascus denied involvement. Washington has since succeeded in largely isolating Damascus, with its European and Arab allies shunning Assad. The last high-ranking U.S. official to visit Syria was then-Deputy Secretary of State Richard Armitage in January 2005. The isolation, however, has begun to crumble in recent months, with visits by U.S. lawmakers and some European officials. Syria treated Pelosi's visit as a diplomatic victory. "Welcome Dialogue," proclaimed a front-page headline in one state-run newspaper next to a photo of Pelosi. Syria's ambassador to the U.S., Imad Moustapha, described the visit as a "positive step" but said "it does not necessarily mean that the U.S. administration would suddenly change its position." In comments to the state-run Al-Thawra daily published Tuesday, he said the visit should be a "reminder that even though we might disagree on politics, we should remain diplomatically engaged in dialogue to reach some understandings." © Copyright 2007 Associated Press. All rights reserved. This material may not be published, broadcast, rewritten, or redistributed.