By JUAN FORERO
 
CARACAS, Venezuela, Aug. 19 - When President Hugo Chávez was ousted in a coup two years ago, the Bush administration celebrated, calling the ouster his own doing. The rest of Latin America was left fuming by the overthrow and expressed strong support for Mr. Chávez as he was almost immediately swept back into power in a popular uprising.

On Sunday, when Mr. Chávez triumphed over his adversaries in a referendum on whether he should be recalled from office, countries from Brazil to Argentina, Colombia to Spain heartily congratulated him. The United States remained silent for more than a day, until a State Department spokesman, Adam Ereli, offered tepid backing for the "preliminary results."

The resounding victory was a blow to the Bush administration, which has struggled with how to deal with Mr. Chávez, a leftist firebrand who presides over the world's fifth-largest oil exporter and has opposed Washington on every major initiative in Latin America. "There's no doubt in my mind that at least in the White House - I don't know about the State Department - there was a deep desire to see Chávez lose," said former President Jimmy Carter, whose Carter Center monitored the election and who has briefed American officials on his efforts to broker a peace between the government and its opponents.

Now, the United States has the challenge of constructing, from the ground up, a new relationship with Mr. Chávez, who has done everything imaginable to antagonize what he calls "the colossus to the north."

He has used an expletive to describe President Bush, threatened to hold back oil sales if the United States invaded, and expanded Venezuela's ties with Cuba. His campaign to win in the vote was built largely on demonizing the United States.

"The Bush government will be defeated on Sunday," Mr. Chávez told reporters three days before the recall vote. "The confrontation in Venezuela is not really with this opposition. The opposition has a master, whose name is George W. Bush."

American diplomats privately say they do not think that Mr. Chávez believes his public statements, and that he manipulates latent anti-Americanism for political gain. But American policy has been largely counterproductive, only contributing to Mr. Chávez's increasingly hostile barbs.

The United States long ago threw its lot in with an opposition movement that is being discredited by foreign diplomats and many Venezuelans for insisting that fraud took place when the preponderance of evidence indicates it did not.

The United States has also provided money to groups like Súmate, which violated elections norms early on Monday by distributing results of a survey of voters leaving the polls that showed Mr. Chávez losing by a wide margin. Mr. Chávez seized on this financing of anti-government groups, channeled through the National Endowment for Democracy, to whip his supporters into an anti-American frenzy.

"The United States is stuck in a time warp," said Riordan Roett, director of Latin American studies at The Paul H. Nitze School of Advanced International Studies at Johns Hopkins University. "It is using tools from the cold war, when money from the National Endowment for Democracy was useful in funding anti-Communist movements."

The United States policy has largely been out of step with the rest of the region. Washington has been unable to grasp the widespread reaction against free market changes across Latin America, changes now being rolled back by left-leaning leaders. In Venezuela, the United States has operated on the presumption that Mr. Chávez's opponents had more support, clearly underestimating that most Venezuelans would vote to keep him in office.

"It's not that the U.S. is not paying attention, it's that their calculation and strategy was wrong," said Eduardo Gamarra, a Bolivian who is director of the Latin America and Caribbean Center at Florida International University in Miami. "And it's been wrong because it's been based on the false assumption that Chávez is not popular, on the false assumption that he's a dictator."

After Mr. Chávez's resounding win, the Bush administration set itself apart from the rest of the region, calling on the Venezuelan government's electoral board to "allow a transparent audit," though international monitors pronounced the election free and fair. On Tuesday, Mr. Ereli, the State Department spokesman, dodged questions from reporters about why the United States was not congratulating Mr. Chávez.

A senior State Department official later said the United States' reticence was intended to defuse tensions in Venezuela, not to dismiss the results. He said Washington would issue a broader statement backing the results after a final audit.

Not all of Washington's diplomatic moves here have failed. Ambassador Charles Shapiro, newly arrived in Venezuela when Mr. Chavez was briefly ousted in 2002, met frequently with him, patching up a relationship that was battered after the White House expressed support for the interim government that replaced him. The United States has also remained a loyal buyer of Venezuelan crude oil. American giants like Exxon Mobil and ChevronTexaco are producing oil and eyeing an expansion into largely undeveloped natural gas fields that are open to foreign investment. Those companies, and other major multinational businesses, provided Venezuela with much-needed foreign earnings when the opposition called nationwide strikes that battered the economy.

Those commercial links can strengthen the bond between Venezuela and the United States, which is dependent on Venezuelan crude.

"The business sector, the large business sector, has understood better the making of foreign policy than our government," Mr. Gamarra said. "They looked at it from the perspective of what business opportunities ought to be.'' Better relations with Mr. Chávez are possible. With his presidency more secure since the vote, he has appeared open to reconciliation. He has invited opposition leaders to lunch and has expressed the wish for a new beginning with the United States.

"I would hope that President Chávez would now cool that anti-U.S. rhetoric," Mr. Carter said. "There's no doubt that Chávez is a charismatic figure, very fiery in his rhetoric, which I deplore. But that's his personal characteristic, one of the avenues of his popularity among Venezuelans. I think now, though, that he is not campaigning for anything."

Steven R.Weisman contributed reporting from Washington for this article.