Witnesses and MENA said Morsi supporters had opened fire during the funeral of a fellow loyalist, but the ousted president's Muslim Brotherhood group denied the claims.
The news agency, citing a local hospital official, said 15 people were wounded overnight by live fire after Morsi supporters began shooting during the funeral in the Suez Canal city.
"Mourners at the funeral of a young supporter of Morsi... opened fire on the Saint George church during the funeral and burned a police car in front of it," Port Said resident al-Tabei Faruq told AFP.
"Morsi's supporters smashed the windows of shops that were displaying pictures of General Sisi," he added of Abdel-Fattah al-Sisi, head of the army that ousted Morsi on July 3.
But Urfa Abu Salmiya, a spokesman for the Brotherhood's Freedom and Justice Party, denied that Morsi supporters started the clashes.
"Some youths attacked mourners at the funeral," he said.
A medical source in Port Said's al-Amiri hospital said five people were being treated there "including two in a critical condition, with bullet wounds to the neck and chest".
Hundreds of Morsi supporters have been holding a sit-in at Port Said's al-Tawhid mosque since his removal by the military following mass protests against him.
On Saturday, at least 72 people were killed in violence at a similar sit-in in Cairo.
Port Said has been a flashpoint for tensions since February 2012, when at least 74 people were killed in a football stadium riot.
HH/HH