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Johnson & Johnson is set to ship nearly four million shots of its single-dose COVID-19 vaccine around the U.S. this week, but a top executive warned Monday that its next round of deliveries will depend on regulatory approvals at a new plant.

J&J's Chief Scientific Officer Paul Stoffels told Reuters Monday that while a new, larger plant run by manufacturer Catalent has been prepping the doses, the U.S. Food and Drug Administration has yet to give them the green light to start shipping.

Stoffels says he expects the Catalent plant to receive approval in the next few days, and believes J&J can fulfill its promise to supply 20 million doses of its COVID-19 vaccine by the end of this month.

Meanwhile, Catalent says it expects approval "in the coming weeks."

J&J Chief Executive Officer Alex Gorsky also told NBC that Americans should begin getting the company's shot as early as Tuesday or Wednesday.

He said he was confident that the J&J vaccine would have a "robust response" against new, more contagious variants of the coronavirus, based on clinical trials in countries like South Africa and Brazil.

The company says it's developing a version of its vaccine to target the South African variant, and will be ready to start late-stage trials by this summer.