Hospital officials said the three unarmed people were not seriously hurt on Tuesday.
The funeral was for a Fatah member killed in a clash with Hamas on Monday.
Fatah officials and witnesses said Hamas set off two bombs and opened fire on the procession, setting off a firefight between the two sides.
Earlier on Tuesday, 10 people were wounded in a gun battle between Fatah and Hamas fighters in Gaza, a day after three were killed in clashes there.
Mahmoud Abbas, the Palestinian president, a senior Fatah member, and Ismail Haniya, who leads the Hamas-dominated government, failed to resolve security problems in talks at the weekend.
Abbas and Haniya, whose Islamist group won parliamentary elections in January, are vying for control of security forces.
Witnesses said that Tuesday's clashes occurred when hundreds of fighters roamed through the Tuffah area of Gaza City.
Four of those wounded were Palestinian teenagers on their way to school, medical staff said. Three armed men were also among the wounded.
Monday's fighting occurred in the southern Gaza city of Khan Yunus and was provoked by allegations that Hamas members had kidnapped at least one Fatah security official.
Keeping the title
Fatah activists were annoyed at the rise to power of Hamas over their faction, which long dominated Palestinian politics but had increasingly been regarded as corrupt.
Hamas, on the other hand, had gained the respect of Palestinians for its aid, education and healthcare programmes.
Fatah, a faction of the Palestinian Liberation Organisation (PLO) has been concerned about losing the title it claimed as its own for decades as the sole representative of the Palestinian people.
Abbas (L) and Haniya failed to
resolve issues in talks on Saturday
Fatah's central committee issued a statement last month condemning any Palestinian faction which does not recognise it as such.
The PLO acquired this capacity in the Arab summit held in Algeria in 1973, and embraced again the Arab summit in Rabat, Morocco in 1974.
Rivalries between Fatah and Hamas deepened after Abbas appointed a Fatah loyalist to a senior post in the interior ministry, which supervises the security forces, so that he could exert more influence over the Hamas-run ministry.
Adding to the tension is a financial emergency caused by the freezing of aid to the Palestinian Authority by donor countries until Hamas renounces the armed struggle against occupation, recognises Israel and signs up to existing peace deals.
Hamas says talks with Israel would be a waste of time.