Florida has invested $850 million in its ports in the last four years, he said. The state has worked to improve and expand its facilities, including in Miami.
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Ports on the East Coast have already cashed in on labor problems. Though the West Coast has historically seen more traffic, Atlantic ports nearly reached parity on so-called containerized imports in February, when West Coast labor groups reached a tentative agreement to end the dispute.
Scott contends that Florida holds a strategic position for maritime traffic and boasts an easier regulatory environment than California.
"We should be the winning state," Scott said.
The Pacific Maritime Association and the California Association of Port Authorities did not immediately respond to requests for comment from CNBC.
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He noted that Florida ports have tough competition with other East Coast cities, including nearby Savannah, Georgia.
—CNBC's Morgan Brennan contributed to this report