Over the past few weeks, U.S. officials have been reported to be in talks with both the Chavez government and the opposition, which is unhappy with the postponement of the inauguration Thursday due to the president's poor health after cancer surgery.
Venezuela is the fourth largest supplier of crude oil to the United States after Canada, Saudi Arabia and Mexico.
Chavez, hospitalized in Cuba, is said to be suffering from severe pulmonary infection and has had trouble breathing, although the latest medical reports indicate his condition is "stationary."
U.S. State Department spokeswoman Victoria Nuland said U.S. officials wished Chavez a full recovery.
Asked for U.S. views on a Venezuelan Supreme Court ruling a postponement of the inauguration would be constitutional, Nuland said, "This is a decision that has to be made by Venezuelans, for Venezuelans, that it has to involve and take into account the views of a broad cross-section of stakeholders."
Nuland said the U.S. administration "will be, obviously, interested in the broader Venezuelan reaction and the conversation that ensues following the Supreme Court's pronouncements.
"But this is something that very much has to be consensual, has to be agreed, has to be transparent, as it moves forward. But it's not a decision for us to make. It's for Venezuelans to make."
The U.S. administration is "willing and open to trying to improve our ties with Venezuela. We've put a number of ideas forward to the government. We've been in conversation about it," Nuland said, citing November telephone conversations between U.S. Assistant Secretary of State Roberta Jacobson and Venezuelan Vice President Nicolas Maduro.
After the news of the talks, Maduro warned the contacts were "distorted" by some news media and insisted Chavez authorized the conversations.
Nuland said: "Regardless of what happens politically in Venezuela, if the Venezuelan government and if the Venezuelan people want to move forward with us, we think there is a path that's possible. It's just going to take two to tango."
Nuland said the stalemate in Venezuelan-U.S. ties was not "personality-based."
Amid uncertainty over Chavez's health, government officials, opposition critics and church leaders argued over interpretations of the Venezuelan Constitution.
Maduro said Chavez's medical condition constitutes an "irrefutable" supervening reason for postponing the inauguration Thursday under Article 231 of the Constitution, El Universal newspaper said.
The opposition says the president's health needs to be independently assessed.
The Catholic Church of Venezuela said it would be "morally unacceptable" for the government to alter the constitution because of Chavez's health.
"At stake are the good of the country and the defense of ethics. To alter the constitution to attain a political objective is morally unacceptable," the Venezuelan Bishops Conference said in a statement read by the group's president, Bishop Diego Padron.
The constitution is clear the current presidential term is to end and a new one is to begin Thursday, the bishops contend.
The bishops added Chavez's extended illness put "at grave risk the political and social stability of the nation."
The stability is made worse, the bishops said, because "the government has not told the people the whole truth (about Chavez's condition), which they have the full right to receive with certitude; it has only communicated, with evident difficulty, its political truth."
The bishops' statement was seen by those in the opposition as supporting their arguments that if Chavez -- who won election to a fourth term Oct. 7 -- cannot be sworn in Thursday, then National Assembly President Diosdado Cabello should become interim president.
But Cabello countered "nowhere" does the constitution state the assembly leader must become president if the president-elect cannot be sworn in Jan. 10.
"The only way is to have 'absolute absence,'" he said, citing the constitutional term for a permanent absence. And so far, he said, there is neither temporary nor absolute absence of the head of state.
"We will do what the people said [in the election] Oct. 7 -- [have] Chavez president of the republic," Cabello said.
Maduro, whom Chavez named as his desired successor before flying to Havana, has argued the presidential swearing-in is a "formality" that can be delayed indefinitely.
And he said the opposition interprets the constitution incorrectly.
Cabello, in a news conference with Maduro, said leaders from "friendly" nations would travel to Venezuela Thursday in a show of support.
"Friendly presidents, heads of government and prime ministers are coming to Venezuela to show their solidarity with Commander Hugo Chavez, with the people and with the constitution," Cabello said.
Uruguayan President Jose Mujica is among Latin American leaders bound for Caracas.