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Most ships should proceed to berth immediately or within a few days, according to the Marine Exchange of Southern California.
ILWU is planning a rally and march against police violence during its regular stop-work meeting.
Rickmers, which manages the ship for Maersk said Iranian navy fired "warning shots" at Marshall Islands-flagged Maersk Tigris.
The stevedoring and ocean freight company's new vessel Marjorie C can carry both containers and roll-on/roll-off cargo.
Ocean carrier Maersk Line says it has not yet received court judgment pertaining to the arrest of the containership by Iranian authorities.
Energy and Water appropriations bill includes infrastructure funding and policy measures favored by the transportation sector.