Planned Parenthood and Affiliated Medical Services sued the state last summer, arguing the requirement will force AMS's Milwaukee clinic to close because its doctors can't get admitting privileges.
The groups argue that would amount to restricting access to abortions in Wisconsin. State attorneys say the mandate will ensure continuity of care for women hospitalized with abortion complications.
Conley has put the law on hold while he weighs the issues. Several states have similar laws, including Alabama, Louisiana and Texas. Abortion clinics have challenged Alabama's mandate in a similar lawsuit.
The judge said Friday he was concerned that the law required providers to get privileges within three days of its enactment. Republican Gov. Scott Walker signed the law on July 5, and it required providers to have privileges in place by July 8.
Conley noted that the law provided no grace period and gave abortion providers no recourse if they couldn't get the privileges. He also said it could dampen clinics' efforts to recruit new providers who would essentially have to come to the clinics with admitting privileges in-hand.
"I remain troubled ... with the inflexibility of the law," he said.
The judge didn't immediately rule on the lawsuit and gave both sides time to file additional arguments, meaning a final ruling isn't expected for at least six weeks.
Conley's comments came after he listened to the two sides' last two witnesses.
Stanley Henshaw, a former researcher at the Guttmacher Institute, an abortion rights research organization, testified that AMS is the state's only clinic that performs abortions beyond 19 weeks of pregnancy.
If it closes, Milwaukee women seeking abortions beyond that point in time would have to travel about 85 miles one-way to a clinic in Chicago, he said.
Henshaw, who testified for Planned Parenthood and AMS, said the distance could prevent poor women who lack resources to travel from getting to a clinic.
Closing the AMS facility would leave the state with three abortion clinics, all run by Planned Parenthood. Henshaw said those facilities wouldn't be able to handle the influx of patients who would have otherwise gone to AMS. That would exacerbate appointment delays that already are stretching out as long as a month, he said.
Testifying for the state, University of North Carolina sociologist Peter Uhlenberg argued that Henshaw's opinions were based on reading articles on abortion rates and distance - none of which claim distance prevents abortion.
He said at least some abortion providers in other states with admitting privilege laws have been able to comply.
During the trial on Thursday, the judge told an AMS doctor to renew his efforts to obtain hospital admitting privileges. Conley said it could help resolve the lawsuit short of a decision on the law's constitutionality.
But AMS's attorneys told Conley on Friday that effort would likely be futile. The hospitals want to evaluate the doctor's experience treating abortion patients in a hospital setting, but since abortion complications are so rare he hasn't treated anyone on an in-patient basis for a decade, they said. Still, they said they've already sent letters to every Milwaukee hospital within 30 miles of the AMS facility asking if his clinic experience would qualify.