Shell used a private shipyard here for repairing its arctic equipment in 2012, which required no public hearings. The difference this time is the involvement by the port, where the commissioners run for office and contracts are public documents. The city’s Department of Planning and Development, under a request sent this week by the City Council and the mayor, is looking at whether the port’s lease, signed with a local company, Foss Maritime, which would manage the terminal site with Shell as the tenant, is consistent with the legal designation of the terminal’s use for “cargo” handling. That decision is expected in a few weeks.

Meanwhile, a lawsuit by the Puget Soundkeepers Alliance and other groups, including the Sierra Club, is challenging the process under which the port reached its decision. In a hearing on Friday before a King County Superior Court judge, the opponents argued that Shell’s use will not be for cargo handling, which is the defined use for the terminal.

The judge, Mariane C. Spearman, pressed lawyers on both sides to explain what exactly Shell would be doing at the site and whether fears of environmental harm were real or speculative, particularly because the rigs are not actually here yet. She said she would rule within the next week whether the case could proceed.

If the lease is revoked, there would probably not be another space on the waterfront big enough to hold the huge rigs, said Mr. O’Brien, the City Council member. A spokesman for Shell, Curtis Smith, said the company had not looked at alternatives. The two rigs Shell plans to bring in — the Noble Discoverer and the Polar Pioneer — are enormous, one more than 320 feet tall and the other more than 500 feet long.

Mr. Smith said the company also remained committed to exploring for oil in the far north. “We have reason to believe the acreage offshore Alaska is home to some of the most prolific, undeveloped hydrocarbon basins in the world,” he said in an email. “As a result, we are advancing our plans to drill in Alaska in 2015 — dependent, of course, on successful permitting, clearing any legal obstacles and our own determination that we are prepared to explore safely and responsibly.”

Shell has spent more than $4 billion on its efforts in the Arctic, but last drilled there in 2012 after a series of setbacks, including the grounding of a drilling rig, the Kulluk, off an island near Kodiak in the Gulf of Alaska. That mishap has also given fuel to opponents like Ian Siadak, who spoke at the lease hearing on behalf of a group formed within the last few weeks called the Coalition for Port Accountability.

“It is up to you whether you will be known as the commissioners who stayed true to their enthusiastically green campaign promises, or the commissioners who sold the planet to Shell Oil,” he said, in demanding that the lease be revoked — within a deadline of two weeks. If that does not occur, he said, “your position will be clear, and we will take further public action.”

Mr. Siadak declined in an interview to specify what action that might be.