The Lima Group, comprising 13 Latin American countries and Canada, is a multilateral body established in August 2017 to focus on Venezuela's situation.
Pompeo also noted that the United States would provide more "humanitarian assistance" to Venezuela, saying the aid was requested by the opposition leader Juan Guaido.
Denying the existence of a humanitarian crisis, the Venezuelan government refused to let the aid cross the border and called the aid operation a U.S.-orchestrated show leading to an eventual invasion.
On Friday night, Venezuelan Vice President Delcy Rodriguez announced the closure of three bridges connecting the country with Colombia. Venezuelan President Nicolas Maduro announced on Saturday the severance of his country's diplomatic and political relations with Colombia, following the latter's support for Venezuela's opposition and military defectors.
"I think we'll find other ways to make sure that food gets to the people who need it," Pompeo said in the interview.
According to a statement issued by the United States Agency for International Development (USAID), the United States has airlifted approximately 191 metric tons of relief supplies to the Colombian border city of Cucuta since Feb. 4.
At the same time, the United States began pre-positioning 178 metric tons of locally-procured supplies in Boa Vista, near Brazil's border with Venezuela, the State Department said Friday.
Venezuelan opposition leader Juan Guaido declared himself "interim president" on Jan. 23 and was immediately recognized by Washington.
In response, Maduro announced he was severing diplomatic and political ties with the United States, ordering all U.S. diplomatic and consular personnel to leave Venezuela.
Maduro has accused Washington of orchestrating a coup d'etat in order to install a puppet regime in Venezuela.