The argument escalated into a brawl which spilled out onto the street where two men — aged 23 and 55 — were stabbed.
Paramedics attended however the pair were declared dead.
Superintendent Janet Stevenson confirmed the two men, both from Seaford, were family but would not go into detail about their exact relationship.
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She said about 20 people were involved in the brawl but several people had left before police arrived.
“We need to talk to those people,” Stevenson said.
“These people hold the key.”
Stevenson could not confirm how many offenders police were looking for and said no weapons had been found.
She said the two men who were killed had a close relationship with the people who were holding the party.
“It’s tragic, you can just imagine how that family feels now — it should have been a great celebration but it’s just a dreadful ending,” Stevenson said.
She urged the people who left before police arrived to come forward.
“‘These people know who they are and it’s in the best interest, especially to this family, for them to contact us as soon as possible and just don’t drag this out, it’s not good for anyone.”
Police are combing through CCTV footage hoping cameras captured the events.
