President Bush's Democratic opponent on Thursday accused him of being too cozy with Saudi Ambassador Prince Bandar bin Sultan (search) to insist that the oil-rich Saudis do more to help lower the cost of gasoline in America.

The Bush camp and Bandar himself deny any undue influence. Bandar said he has talked about oil with Bush just as he has with Bush's predecessor, Bill Clinton (search), and other U.S. presidents going back to Jimmy Carter (search).

The U.S. dependency on foreign oil — and the fact that Saudi Arabia has more crude than anyone else — has compelled all presidents to befriend the Middle Eastern country. As Bandar told CNN earlier this week, "Oil prices and Saudi Arabia and American politics are intertwined."

That, precisely, is why Kerry's gambit could prove effective, said Saudi Institute analyst Ali al-Ahmed.

"Any association between the Bush family and the Saudi royal family is only going to undermine the credibility of the president," al-Ahmed said. "I think Bush either has to dance around it somehow, or join Kerry in his rhetoric — especially if Kerry is going to receive support from many people in the United States who do not like Saudi Arabia very well."

In an Earth Day speech Thursday, Kerry criticized a meeting in which, according to a broadcast report, Bush and Bandar discussed increasing oil production as the election nears. Kerry said that flew in the face of Bush's 2000 campaign pledge to lean on OPEC nations about making more oil.

"I don't know if it was a deal, I don't know if it was a secret pledge, I don't know if it was just a friendly conversation among friends," Kerry said. "The fact remains that whatever it was, the American people are getting a bad deal today."

Kerry was clearly looking to exploit the long-standing relationship between the Saudi government and Bush's family. Bush's father, former President George H.W. Bush, was especially friendly with Saudi officials, an alliance that grew warmer during the early 1990s before and during the Persian Gulf War.

The Saudi ambassador was on hand when the elder Bush's official portrait was unveiled at the White House in 1995, and he was a guest at a surprise 75th birthday party in 2000 for former first lady Barbara Bush in 2000. The former president also has vacationed at Bandar's home in Aspen, Colo.

Bandar has been a guest at the Bush ranch in Crawford, Texas. Last year, he presented the first family with a C.M. Russell painting, a gift worth $1 million that will be stored in the National Archives, along with other presents from well-wishers destined for a Bush presidential library.

Bush called on his father in April 2002 to smooth over rockiness in U.S.-Saudi relations after the Sept. 11, 2001, attacks, which were carried out by 19 terrorists — 15 of them Saudis. After meeting in Texas with the president, Saudi Crown Prince Abdullah took a nearly two-hour private train ride with the elder Bush and got a private tour of the Bush presidential library.

Bush's father was closer to the Saudis than his son. While friendly, the president has lent strong support to Israel in spite of Arab complaints.

Good relations with the American public at large also matter to the Saudis. After the Sept. 11 attacks, the Saudi government spent $17 million on public relations, advertising and lobbying to promote U.S.-Saudi friendship.

Yet many U.S. critics contend the Saudis have not done enough to crack down on terror financing in their kingdom.

Bandar, a familiar figure in Washington, has met Kerry on official and social occasions, too, said Stephanie Cutter, the senator's spokeswoman. "I would not describe it as a close relationship," she said.

Philip Wilcox, a former U.S. diplomat who is now president of the Foundation for Middle East Peace, said personal ties between U.S. and Saudi officials go back to at least 1945, when President Franklin Roosevelt met with King Abdul-Aziz, who had united Saudi Arabia and was its first ruler.

That history, Wilcox said, is why U.S. politicians must walk a fine line with the Saudis — both in cultivating ties and criticizing them.

"These competing interests cannot all be reconciled," Wilcox said. "Saudi Arabia is a friend and ally. (Oil) is their livelihood. They're not an extension of the United States, or a client of ours. We shouldn't expect them to reduce their national income just to provide cheap energy for us."