The deceased were identified as Azizul Chowdhury, 40, son of Mosharref Chowdhury of Singati village, and his paternal uncle Mursalin Chowdhury, 30, son of Ershad Chowdhury.
Police said the injured were receiving treatment at Mollahat Upazila Health Complex, Khulna Medical College and Hospital and Gopalganj Sadar Hospital.
Locals said a longstanding dispute had existed between Ershad Chowdhury and his cousin Masum Chowdhury of Singati village over establishing dominance in the area.
The two groups had clashed several times in the past over the issue.
On Eid day, an argument erupted between the groups over the distribution of sacrificial meat.
Later in the evening, supporters of both sides engaged in a violent clash using locally made weapons, leaving 32 people injured.
Azizul was declared dead upon arrival at Gopalganj Sadar Hospital, while Mursalin succumbed to his injuries while undergoing treatment at the same hospital around 10pm.
Both were reportedly followers of the Ershad group.
Md Shafiqur Islam, officer-in-charge of Mollahat Police Station, said they rushed to the spot upon receiving information and brought the situation under control.
Additional police forces have been deployed in the area to prevent further violence, he said, adding that no written complaints had been filed as of yet, reports UNB.
Efforts are underway to arrest those involved in the killings, the OC added.