* Senior diplomat spoke with VP Maduro last November
* Ties between nations have been fraught for years
WASHINGTON, Jan 9 (Reuters) - The United States said on Wednesday it would like to improve relations with Venezuela, gripped by political uncertainty following socialist President Hugo Chavez's fourth cancer operation, but it will "take two to tango."
Venezuela has said it would postpone Thursday's scheduled inauguration for Chavez, 58, who has not been seen or heard from since surgery in Cuba on Dec. 11. He was diagnosed with an undisclosed type of cancer in his pelvis in June 2011.
The unprecedented silence by the president, a fierce U.S. critic famous for speaking for hours in meandering broadcasts, and the postponement of his inauguration for a third six-year term has left many convinced he could be in his last days.
While she did not tie it to Chavez's ill health, U.S. State Department spokeswoman Victoria Nuland said the United States had long been interested in improving ties with Venezuela, an OPEC member and historically the United States' fourth-largest supplier of imported crude oil and petroleum products.
She also confirmed media reports that Roberta Jacobson, the senior U.S. diplomat for Latin America, spoke by telephone in November with Venezuelan Vice President Nicolas Maduro, Chavez's heir apparent, about improving ties.
"We have for some time made clear that we were willing and open to trying to improve our ties with Venezuela. We've put a number of ideas forward to the government," Nuland said at her daily briefing, without detailing the U.S. proposals.
"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," she added. "It's just going to take two to tango."
The spokeswoman declined to comment on the constitutionality of the Venezuelan government's decision to postpone Chavez' inauguration, a move that was endorsed by the country's Supreme Court on Wednesday, saying this was for Venezuelans to decide.
Ties between the two countries have been tense for years for many reasons, including Chavez's fiery criticism of the United States and Washington's misgivings about his nationalizations of industry and what it regards as his authoritarian tendencies.
The countries do not have ambassadors accredited to one another.
In 2010 the U.S. government revoked the visa of Venezuela's ambassador to the United States in retaliation for Chavez's rejection of a nominated U.S. envoy critical of his government.
Despite the tensions, Venezuelan oil has continued to flow to the United States.
In a background note posted on its website in April 2012, the State Department said the United States continued to seek constructive engagement with Venezuela's government, focusing on areas where cooperation was in both countries' interest.
"Examples of such overlapping interests include cooperation in confronting narcotics trafficking and terrorism, as well as the commercial relationship," the note added.