Unifor says it successfully lobbied to get Ready appointed to the dispute.
Federal Transport Minister Lisa Raitt agreed to the request
"We're fully prepared to stay in discussions until this dispute is resolved," said Paul Johal, the president of Unifor - Vancouver Container Truckers' Association.
"If we can't make progress at the table today on key issues, we'll have no other option but to put up picket lines."
Unifor is concerned about long line-ups and wait times, which it says are costing its drivers money.
It is demanding increased pay rates and wants the rates standardized and enforced across the trucking sector to put an end to under-cutting.
Both sides far apart
Both sides agree it takes too much time for truckers to drop off and pick up cargo at the port's four shipping terminals.
However, no one agrees on how to fix the problem. Truckers want higher rates to compensate for long wait times, but the port and trucking companies want to extend operating hours to speed things up.
Tempers flared on Sunday night in the dispute when a driver with a Delta trucking company was reportedly hit in the head by a large rock as he was driving 70 km/h along Highway 17.
The rock flew through the driver's side window, shattering the glass and cracking the windshield on the opposite side.
Some $885 million worth of cargo moves through the port every week, about $46 billion a year, said Raitt's office Thursday in a statement on the dispute.
The port says it is already feeling the effects of work stoppages begun by some non-unionized truckers — effects that could be worsened if unionized truckers were to follow through with job action.