The prime minister and the premier offered contradictory messages two days after hundreds of unionized truckers parked their rigs to back demands related to pay. Those workers joined roughly a thousand non-unionized truckers who walked off the job last month.
Harper, fresh from a trip to South Korea, where he signed a free-trade agreement, said the labour dispute at the port was jeopardizing trade with Asia.
"We're obviously concerned about this particular labour dispute ... and it is not acceptable to have relatively small numbers of people blocking what is important trade for a range of British Columbian and Canadian business," Harper said during in a friendly question-and-answer session in front of a business audience at a downtown Vancouver hotel.
"Unfortunately, the labour disputes here are really under the jurisdiction of provincial government, not ours."
Last week, the federal government appointed a veteran labour mediator, Vince Ready, to review the dispute and examine the broader labour issues within the trucking industry. He is due to report back to the federal and provincial governments by the end of May.
Beyond that, Harper suggested his hands were tied.
But Clark made it clear the B.C. government sees things differently. She suggested it was up to Ottawa to bring the strike to an end, and she urged the federal government to move quickly.
"It (the strike) is absolutely unacceptable — it poses a huge economic problem, not just for our province but for our country," Clark told reporters at the legislature in Victoria.
"My advice to the federal government is this: almost all of the elements of this dispute, which are licensing and rates, lie solely within federal jurisdiction. (Transport) Minister Todd Stone has been working every single day to be in contact with the federal government to urge them to make sure they move as quickly as possible on this."
She stressed that time was of the essence: "We would like it solved today, yesterday, the day before yesterday."
Neither Harper nor Clark explained just what they would like the other's government to do.
Port Metro Vancouver administers the region's port system, leasing government-owned land and terminal space to private operators.
It is Canada's largest port, moving more than $170 billion worth of goods each year. Trucks transport about half of the containers that move in and out of the port, while the rest are moved by rail.
The striking truckers are not employed directly by Port Metro Vancouver; rather, they are either independent contractors or sub-contractors working for trucking companies.
On the first day of the strike, the port's container terminals saw just 10 per cent of its normal truck traffic. Port spokesman John Parker-Jervis said that had improved to 15 per cent.
"Cargo that's come in and can't get out would be sitting at one of the terminals, but the other 50 per cent is still leaving by rail, so that continues on," said Parker-Jervis.
"It mostly will affect the cargo that's coming to the local market here or that has some sort of value added here in the Lower Mainland."
The unionized workers have a collective agreement with their employers, while an agreement that was put into place after a strike in 2005 sets minimum rates for non-unionized truckers.
Paul Johal, president of the Vancouver Container Truckers' Association, a branch of Unifor that represents the unionized port truckers, disagreed with how the prime minister characterized the strike.
"That's his own opinion, I guess," Johal said in an interview Wednesday.
"We're not blocking anybody. We're not stopping anybody. We're just protesting outside the port."
Johal said no negotiations had been scheduled, but the truckers are eager to resolve the dispute.
The Vancouver Container Truckers' Association has been negotiating a new collective agreement since 2012. The primary issues are wages and compensation for the time drivers wait at the port for their cargo.
Last week, it appeared the strike by unionized workers had been averted, when Unifor announced it had reached a tentative agreement with the truckers' employers, but the workers overwhelmingly voted to reject the offer.
— With files from Dene Moore in Vancouver and Dirk Meissner in Victoria
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