West Yorkshire police say that three men had broken into the house in Hetton Road in Oakwood, between 7.20pm and 7.50pm on Wednesday November 7 and that the householder and her two sons, aged five and six, returned home during the incident and noticed a light was on.
As she entered the house, the suspects were coming down the stairs and pointed a knife towards one of the children and said: “Come any closer and we will kill him”.
The men, who were wearing balaclavas and dark clothing, escaped through the rear patio doors which they had broken in through, and fled over the garden fence.
They stole Asian gold jewellery with a "significant value", added a police spokesperson.
PC Joe Carlisle, of Leeds District Crime Team, said: “This was a very distressing experience for the victim and her young sons and we would like to hear from anyone who witnessed anything suspicious in the area at the time or who has any information that could assist the investigation.
“Asian gold jewellery with a high value was taken during this burglary and we would like to hear from anyone who has been offered such items for sale in suspicious circumstances.”
Anyone with information is asked to contact PC 3860 Carlisle at Elland Road via 101 quoting crime reference 13180559771 or call the independent charity Crimestoppers anonymously on 0800 555 111.