WASHINGTON – President Bush congratulated King Abdullah on his accession yesterday as the White House adjusted to the second major change to the American-Saudi alliance in a fortnight.

The bond between the two nations was for decades the cornerstone of Washington’s policy in the Arab world. It reached new levels of coziness under the first President Bush during the Gulf War when the cigar smoking and whiskey-drinking Saudi ambassador to America, Prince Bandar bin Sultan, a confidant of King Fahd, earned the nickname Bandar Bush.

But in recent years the American-Saudi nexus and indeed the relationship between the Bush clan and the House of Saud have become more complex. After the September 2001 attacks, Washington’s hawks seized on the fact that most of the hijackers were Saudi to call for a re-examination of ties to an ally they regarded as at best fickle and at worst an incubator of terror.

With the invasion of Iraq they saw an obvious alternative source of oil to keep the heartland’s cars on the road.

Yesterday’s White House statement of staunch support, however, was a reminder of how the relationship has shifted again as American forces have become bogged down in Iraq.

“We have a close partnership with Saudi Arabia and good relations,” a White House spokesman, Scott McClellan, said after Mr. Bush telephoned the new Saudi leader. In April Mr. Bush hosted the then crown prince at his ranch in Texas.

Diplomats are confident King Abdullah, the de facto ruler for the last 10 years, will not use his formal assumption of power to change policy. But it has long been apparent he does not have the same close relationship with the second President Bush that King Fahd had with the first.

Two weeks ago Riyadh sent a clear signal that the old American-Saudi era was over when it confirmed that Prince Bandar was stepping down as envoy in Washington.

“This has historically been such a close relationship,” said Craig Unger, author of “House of Bush, House of Saud.” “You don’t have that close relationship any more.”