A judge trying Deborah Parry and Lucille McLauchlan asked the victim's family to consider accepting a settlement rather than request the death sentence.
Under Islamic law, which is enforced in Saudi Arabia, the victim's family has the right to demand a public beheading or accept blood money.
Frank Gilford, the brother of the murder victim, Australian Yvonne Gilford, has previously refused to waive the death penalty. Through lawyers, he insisted when the trial opened that he would not accept a monetary settlement even if the British nurses' families decided on a plea of clemency.
But judges decided to adjourn the trial for three weeks to permit further consultation with Mr Gilford, although there is still evidence to be heard.
A court official, who spoke on condition of anonymity, said that if they were convicted, the only way to avoid the death sentence might be an appeal from Mr Gilford for clemency.
The Salah Hejailan law firm representing the woman said that the judge asked the victim's family "to accept as a principle that it may be possible to reach a conciliatory settlement."
Ms Parry, 41, from Alton, Hampshire, and Ms McLauchlan, 31, from Dundee, have both denied murdering 55-year-old Ms Gilford.
Her body was found on 11 December last year on the floor of her flat in the King Fahd Military medical complex in Dhahran, where all three lived and worked. Ms Gilford was reported to have been stabbed, bludgeoned and suffocated.
The latest development came on a day when the lawyers had been expected to argue that it was the brutal treatment the nurses received from Saudi police officers which led them to break down and make false confessions.The nurses had been expected to tell the court that the confessions should not be used against them because they confessed after policemen stripped them and threatened to rape them.
Both nurses retracted their confessions soon after being charged with the murder of Ms Gilford last December and repeated the retraction, through translators, at the trial's opening session last week.
The court in Al-Khobar, eastern Saudi Arabia, sat for only an hour yesterday before adjourning.
In a statement, the defence lawyers said that the women "were concerned at the three-week delay and were impatient to be allowed... to give their account to the court."
The lawyers presented 18 pages of evidence and legal documents in the women's defence to the court yesterday.
Ms Parry and Ms McLauchlan had arrived at the four-storey courthouse in separate police vans.
They were dressed in traditional black Saudi cloaks, but were not wearing the iron shackles used at last week's hearings. A number of human rights groups had objected to the shackles.
Security around the courthouse was the tightest since the start of the trial. Undercover policemen confiscated a photographer's camera and briefly detained a reporter.