Negotiators for nurses met with a mediator Monday as a strike at AMITA Health Saint Joseph Medical Center Joliet went into its 10th day.
Nurses on Saturday voted 393 to 154 against AMITA's latest contract offer.
The Illinois Nurses Association said nurse staffing levels at the hospital remained the major issue of contention.
The INA met with a mediator, who has been involved in the bargaining for weeks, to present options aimed at resolving the staffing issue, said Pat Meade, a nurse at the hospital and member of the negotiating team.
"We've been working on something for staffing because we will not budge," Meade said. "We have been floating ideas through the mediator to take to their lawyer."
AMITA on Sunday issued a statement saying it believed the proposal rejected by the nurses was "fair and balanced, addressing the criteria the INA indicated were important to its members."
The INA represents 720 nurses at the hospital.
AMITA has brought in replacement nurses, busing them into the hospital during the strike.
The two sides have had one one bargaining session since the strike began, which led to the proposal rejected by the nurses. But they have also sent proposals back and forth on days when no sessions were scheduled.