(CNN) Secretary of State Mike Pompeo said that the United States would take further action to pressure embattled Venezuelan President Nicolas Maduro after several people were killed in clashes with the country's military blocking humanitarian aid from entering the country.

"There's more sanctions to be had. There's more humanitarian assistance, I think, that we can provide," Pompeo told CNN's Jake Tapper on "State of the Union" Sunday. "I think we'll find other ways to make sure that food gets to the people who need it, and we will."

Pompeo added that "further action will be contemplated" at a meeting Monday of the Lima Group, the diplomatic body established in 2017 to help mitigate the Venezuelan crisis.

He also pushed back against critics alleging that the White House was using the aid as a negotiating tool to spur a regime change.

"This aid went in ... at the request of the legitimate president of Venezuela," Pompeo said, referencing US-backed opposition leader Juan Guaidó. "He said, 'Please bring food to my people. Please bring medicine to the sick that are here.' That's what we've been working on these past few weeks."

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