Secretary of State John F. Kerry attends the Organization of American States General Assembly in Santo Domingo, Dominican Republic, on Tuesday. (Evan Vucci/AFP/Getty Images)

The United States and Venezuela will work to improve their strained relations, Secretary of State John F. Kerry said Tuesday after meeting with his counterpart from Caracas, who hours earlier had accused Washington of helping foment a coup against Venezuela’s socialist government.

On a day that started with Kerry backing calls for a referendum to recall President Nicolás Maduro, as well as Venezuelan Foreign Minister Delcy Rodriguez saying Washington was “bullying” her country, Kerry and Rodriguez spoke privately for about half an hour. Initially they avoided eye contact when posing for photos and exchanged an awkward handshake, but Kerry later described their conversation as “very congenial and very respectful.”

Kerry said the United States does not support suspending Venezuela from the Organization of American States, one possible outcome of a push by OAS Secretary General Luis Almagro, who has accused the Maduro government of failing to live up to the group’s Democratic Charter. Rather, Washington supports mediated talks with the Maduro government’s opponents as Venezuela continues to be roiled by food and medical shortages, high inflation and anti-government protests.

“That wouldn’t be constructive,” Kerry said of a suspension. “It’s more constructive to have the dialogue than to isolate.”

Kerry said he would dispatch Thomas A. Shannon Jr., the undersecretary for political affairs, to Caracas “immediately” for talks. He also suggested that improved relations between the two countries depend on whether Maduro acquiesces to opposition calls for a recall referendum.

“We are supporting it in the context of a constitutional prerogative that is available to the opposition, which they have chosen to exercise and have been frustrated in the exercise,” Kerry said.

Asked whether Maduro would be open to dialogue with the opposition, Kerry said that he had talked it over with Rodriguez and that “she indicated that he wants to proceed in this direction, and we will explore that.”

“I’m committed to see if this can work, so let’s see if we can improve the relationship,” he said.

Kerry’s soothing words appeared to be an attempt to tone down a fiery start to the OAS General Assembly meeting here.

Kerry opened the session decrying the “deeply troubling” situation in Venezuela, citing reports of people dying while queuing in long lines for food and medical care.

“Like all people of the Americas, Venezuelans have the right to use constitutional mechanisms to express their will in a peaceful and democratic manner,” Kerry said. He then called on the Venezuelan government to release political prisoners, respect freedom of expression and assembly, and honor petitions for a recall referendum.

Moments later, Rodriguez responded with harsh words against both Washington and the OAS secretary general over his proposal to suspend Venezuela from the 34-state organization.

Calling Almagro “biased” in favor of her country’s political opposition, Rodriguez said the secretary general’s efforts prove he is intervening in the country’s domestic politics.

“I see now this is ordered by Washington,” she said, adding of the OAS, “I know they are on Washington’s payroll to meddle in the domestic affairs of Venezuela.”

Rodriguez trained her anger further on the United States, which she said has shattered the Middle East and Africa.

“Today, Venezuela is the victim of international bullying from the right,” she said, blaming nations that “seek to overthrow progressive left-wing governments in our region.”

Venezuela is spiraling toward chaos. Low prices for oil, the financial bedrock of Venezuela’s socialist domestic programs and its regional political power, have hurt the country’s ability to import goods, causing shortages of food, medicine and other products. Electrical blackouts are so severe that Maduro has urged women to stop blow-drying their hair.

Maduro has responded with what critics call growing authoritarianism. He declared a state of emergency that has allowed him to throw critics in jail, undercut the independent press and suppress the opposition in the National Assembly. Anti-government protesters have been repelled by security forces in Caracas.

A June 23 meeting of the OAS has been called to discuss a 132-page report that Almagro released last month and that reads like an indictment of Maduro’s government. Almagro needs a majority, or 18 votes, to agree with him that “there is an alternation in the [Venezuelan] constitutional order that seriously affects the democratic order.”

The United States supports Almagro’s efforts, which Kerry said “will open a much-needed discussion about Venezuela” that could ultimately help ease the pressures that have led as much as a third of Venezuela’s 30 million residents to say they want to leave their country.

Since Almagro became head of the OAS last year, he has increased the organization’s focus on democracy and human rights. Washington pays 60 percent of the OAS budget and is home to its headquarters.

Although the crisis in Venezuela is not officially on the agenda of the General Assembly, it is dominating many of the private discussions.

According to diplomats at the assembly, the United States is floating a draft statement seeking support for the measures Kerry outlined in his speech. Washington can expect support from Canada, Mexico, Chile, Uruguay and Brazil.

In return, Venezuela is circulating a draft that calls for the United States to apologize for its 1965 invasion of the Dominican Republic. That year, President Lyndon B. Johnson ordered 22,000 U.S. troops into the country to prevent what he called the establishment of a “communist dictatorship.” Caracas has its own list of allies, including Bolivia, Ecuador, Nicaragua, El Salvador and several small Caribbean countries that receive heavily discounted oil from Venezuela.

The fracas at the OAS over Venezuela has grown intensely acrimonious in recent weeks. Maduro has accused Almagro of being a CIA agent, and told him to roll up the OAS Democratic Charter in a vial and “stuff” it. Almagro has accused Maduro of being a traitor to his people and being on the path to becoming a “petty dictator.”

In his morning remarks, Kerry expressed disappointment that the Dominican government had barred representatives of civil organizations from attending the General Assembly.

“Transparency and citizen participation are not optional, and they are not prerogatives of the host government,” he said.