Some Texas abortion clinics have reopened amid fears that a legal ruling which halted the state's near-total abortion ban may be short-lived.
Other clinics have reported that concerns over lawsuits have prevented them from reopening.
On Wednesday, a US judge temporarily blocked the new law, which effectively bans women from having an abortion.
Texas officials appealed against the ruling, setting the stage for further court battles in the coming months.
Abortion care provider Whole Woman's Health, which runs four clinics across Texas, said it had already resumed offering abortion care on Thursday.
Speaking to reporters, Amy Hagstrom Miller, the firm's founder, said there had been an immediate spike in inquiries from patients seeking abortions in the wake of the judge's decision.
"Phone call volume has increased. There's actually hope from patients and staff," she said. "There's a little desperation in that hope. Folks know this opportunity could be short-lived."
District Judge Robert Pittman's 113-page ruling earlier this week granted a request from the Biden administration to prevent enforcement of the law while its legality was being challenged.
This is the first legal setback for Texas since the law - which was drafted and approved by Republican politicians - was implemented.
The law effectively bans abortions from as early as six weeks into a pregnancy, at a time when most women will not be aware they are pregnant.
Despite the injunction, some clinics remain hesitant to resume procedures as there is uncertainty over whether they could be sued retroactively if the law is re-instated.
The controversial law can be enforced by any individual from Texas or elsewhere, giving people the right to sue doctors who perform an abortion past the six-week point. Women who get the procedure, however, cannot be sued.
The law includes a provision that stipulates clinics and doctors may still be liable for abortions carried out while an emergency injunction is in place, legal experts say.
It remains unclear whether such a provision can be enforced, with Judge Pittman saying in his ruling that it is "of questionable legality".
Ms Miller said that both patients and staff at Whole Woman's Health were worried about the possibility of retroactive lawsuits.
Other abortion clinics said they were taking a cautious approach to resuming abortion care services.
Sources within Planned Parenthood's affiliate South Texas - which operates seven clinics in San Antonio and the Rio Grande Valley - said that it remained unclear when they would resume providing abortion care.
Among the factors preventing an immediate restart of services, sources said, are concerns about retroactive lawsuits along with the possibility of trauma for patients who may get an appointment while the emergency injunction is in place but are forced to cancel later.
An abortion doctor working at an independent facility in Texas - who asked to remain anonymous - told the BBC he and other reproductive specialists were "not optimistic" about the possibility of the appeal from Texas officials.
"We're going right back to where the law was on 1 September. This will be the most conservative appeals court in the US," he said, referring to the conservative-leaning Fifth Circuit Court of Appeals, where Texas intends to appeal the ruling.
"They're going to overrule the federal judge, and it's going to go back to where it was, and we're going to be in the same boat."
Supporters of the law have harshly criticised the judge's decision.
The anti-abortion group Texas Right to Life, for example, accused judges of "catering to the abortion industry" and called for a "fair hearing" at the next stage.