A city judge was set to preside over an emergency hearing on the injunction request Friday afternoon.
Commuters have been dealing with clogged roads, jumping on bikes and organizing carpools around the city while more than 50,000 city children have to find other ways to get to school.
"We have to get this done. Too much is at stake," said Carla Showell-Lee, spokeswoman for the Southeastern Pennsylvania Transportation Authority.
The Transport Workers Union local did not immediately respond to the injunction request. Transit workers hit the picket lines again Friday while negotiations continued.
The state Supreme Court previously has upheld injunctions to end transit strikes over the public's health and safety, especially when it comes to the ability of police, fire and ambulance crews to get around.
SEPTA argues that the elderly, disabled and ill are in danger of losing access to needed services. It also argued the strike would make it difficult for people who vote before or after work given the added commuting times the strike has caused.
On Thursday, the authority asked for assurances from the union that it would suspend its walkout on Election Day if no contract agreement is reached by then. Pennsylvania is a battleground state, and the vote in overwhelmingly Democratic Philadelphia is critically important to Democratic presidential nominee Hillary Clinton as she battles Republican Donald Trump.
The union's 4,700 workers walked off the job after midnight Monday, shutting down transit service that provides about 900,000 rides a day. Pensions, work rules and health care costs are among the issues on the bargaining table.
The walkout is the ninth since 1975 by the city transit union. The last one, in 2009, lasted six days. Some have lasted for weeks.
Copyright 2016 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.