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Rickmers, which manages the ship for Maersk said Iranian navy fired "warning shots" at Marshall Islands-flagged Maersk Tigris.
A strike could come as soon as Monday, according to a statement from Teamster affiliate Justice for Port Truck Drivers.
Most ships should proceed to berth immediately or within a few days, according to the Marine Exchange of Southern California.
Trade Promotion Authority, a bill that grants the president authority to conclude trade deals without congressional interference, moved forward in the Senate Thursday morning.
Three of the biggest U.S. retailers have said maintaining in-stock levels was a challenge in first quarter 2015 because of West Coast port disruption.
The Southern California port plans to acquire 3,000 container chassis in two steps.