"The Council very unlikely will be able to agree today," Pierce said on Thursday.
Later in the day, the UN Security Council is set to vote on the dueling draft documents on the situation in Venezuela submitted by Russia and the United States.
The document introduced by Russia reaffirms Venezuelan President Nicolas Maduro government’s role in coordinating aid delivery, appeals for political dialogue, including through the Montevideo mechanism, and urges against the use of force against the Bolivarian Republic.
Tensions in Venezuela escalated on January 23, when opposition leader Juan Guaido declared himself interim president. Incumbent President Nicolas Maduro qualified Guaido's move as an attempt to stage a coup orchestrated by Washington.
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The United States immediately recognized Guaido, and around 50 other countries followed suit. Russia, China, Cuba, Bolivia and a number of other countries have meanwhile voiced their support for the legitimate government of Maduro.
On Saturday, the opposition failed to force unauthorized US-sponsored aid into Venezuela. Maduro told ABC News this week that the United States is fabricating a crisis to justify military intervention in Venezuela.