DAMASCUS, April 4 (Reuters) - U.S. House Speaker Nancy Pelosi met President Bashar al-Assad on Wednesday, against White House wishes, to urge Syria to help stabilise Iraq and stop supporting Washington's adversaries in the Middle East.

Pelosi, the third most senior U.S. official, sat next to Assad in front of cameras before starting a meeting at his hilltop palace overlooking Damascus.

The White House has described her visit as a bad idea.

A member of Pelosi's delegation said she would raise during the meeting Syria's suspected support for anti-U.S. rebels in Iraq and its backing for Palestinian movement Hamas and Lebanon's Hezbollah.

Syrian officials said Damascus wants to help Washington achieve an "honourable withdrawal" from Iraq but in return the United States must press Israel to return the Golan Heights, which the Jewish state captured in the 1967 Middle East war.

"Pelosi's visit won't be enough to remove all obstacles in the form of normalising American-Syrian relations, but we believe that the dialogue she is conducting in Damascus is very important," government newspaper Tishreen said.

"Syria's position is rejection of the Iraq war. We are concerned about Iraq's stability and unity because Syria is the main casualty of the chaos, violence and terrorism there," Tishreen said.

The newspaper was referring to 1.2 million Iraqi refugees, who, according to Syrian estimates, have fled to Syria since the U.S.-led invasion four years ago.

Pelosi, on a Middle East tour, said on Monday she had "no illusions but great hope" for the talks which she said would focus on the fight against terrorism, Iraq and Lebanon.

The White House has condemned Pelosi's plans to visit Syria and meet Assad, who the United States has accused of helping destabilise the region, saying it sent the wrong message to the Syrian leader.

The U.S. embassy hosted a big reception for Pelosi on Tuesday night that was attended by three Syrian government officials as well as dissidents who said they were not allowed enough access to Pelosi, who championed the cause of human rights in China.

Pelosi has shrugged off the White House's criticism of the trip, saying it was a good opportunity to gather the facts and build confidence.

The United States withdrew its ambassador from Damascus shortly after the assassination of former Lebanese Prime Minister Rafik al-Hariri in February 2005.

Several U.S. lawmakers visited Damascus and met Assad in the last few months after the bipartisan Iraq Study Group recommended a stepped-up diplomatic effort involving Syria and Iran to help calm the violence in Iraq.

The Bush administration has resisted that recommendation.