Palestinian sources said that the Israeli navy fired on a fishing boat that had strayed outside of a six nautical mile fishing zone off the coast of the Gaza Strip, Israel Radio reported on Wednesday.
The fishermen jumped overboard as the naval fire tore the boat to pieces. There were no reports of injuries.
On Monday officials from the Hamas-run security services said two Gaza fishermen were wounded and four missing Monday after the Israeli navy fired on two boats off the coast.
It was not immediately clear whether the four had been arrested, the officials added.
The IDF confirmed that naval fire had destroyed one boat it said had been involved in smuggling, but had no information about the four fishermen reported missing.
The two wounded fishermen were pulled out of the water off the southern port of Rafah after the Israeli fire destroyed both boats, a Hamas security official said.
According to Israel Radio since the end of Operation Protective Edge in August there have been numerous incidents of Palestinian boats straying beyond the six-mile limit.
Under the terms of an August 26 truce agreement which ended a deadly 50-day war between Israel and Hamas militants, Gaza fishermen, who number around 4,000, are permitted to trawl the waters up to six nautical miles off the shore.
AFP contributed to this report.