PORTLAND, Ore. >> Portland leaders are trying to make Uber’s stay a short one.

The city sued the online ridesharing business Monday, asking a judge to order the San Francisco-based company to cease operations here.

Uber launched its ride-sharing app in Portland at 5 p.m. Friday. Demand was reportedly high and the new competition appeared to trigger a weekend uptick in the number of traditional taxis in and around downtown.

Uber spokeswoman Eva Behrend said in a statement that nearly 7,000 Portlanders signed a petition in support of Uber in four hours Monday.

“Uber continues to operate and looks forward to meeting the tremendous demand that we have already seen in just three days since launching in the Rose City,” she said.

The ride-sharing company has run up against taxi regulations in many other cities, where sometimes its operations have been accommodated.

Uber has said it isn’t bound by rules governing traditional taxi companies. Uber’s drivers are independent contractors, and the company takes a cut of fares.

In Oregon, Uber began operating in Salem and Eugene last summer and in Portland suburbs this fall.

When it launched in Portland last week, City Commissioner Steve Novick threatened to “throw the book” at the company for violating rides-for-hire regulations.

Uber drivers accepted and then canceled two rides requested by Portland Bureau of Transportation enforcement officials Friday night. The following night, drivers provided three rides to code enforcers, the city said.

The Transportation Bureau issued two civil penalties to Uber on Monday, one for operating without a company permit and another for operating without a vehicle permit.

“If Uber thinks there should be no maximum price on what they charge Portlanders, they should make their case to the Portland City Council,” Novick said Monday. “If Uber thinks taxi companies shouldn’t have to serve people with disabilities, they should make their case. If Uber thinks taxis should not have to have proper insurance in case of a crash, they should tell us why we should allow that.”

In a separate action, a city attorney sent a letter telling Uber to stop using an image of the well-known “Portland, Oregon,” sign in its advertising.