Jurors in the trial of Lindsay Clancy are deadlocked after three days of deliberations, but a judge has asked them to keep trying.

Clancy, a resident of Massachusetts, is facing murder charges for killing her three children at their family home in 2023.

Her lawyer does not dispute that the 36-year-old former nurse killed the children, but argues that she was suffering from postpartum psychosis at the time and was unable to distinguish right from wrong.

After discussing the case for several more hours on Tuesday, jurors were sent home for the day and asked to return on Wednesday.

"I just want to thank you for all your hard work and commitment so far in this case," the judge told jurors before sending them home.

The Massachusetts mother is charged with three counts of first-degree murder, as the prosecution argues she made a calculated, intentional decision to kill them.

The jury, made up of nine women and three men, began deliberating last week after hearing weeks of testimony from dozens of witnesses.

On Tuesday, audible gasps could be heard in the courtroom as Judge William Sullivan read out a note from the jury indicating that it was deadlocked.

Clancy, who was left paralysed after jumping from a second-floor window shortly after the killings, appeared stoic as she sat in a wheelchair beside her lawyer.