This is the latest exchange as part of a US-brokered ceasefire reached last month, whose first phase is winding down even as violence continues in Palestinian territories.
The Israeli military said an "armed terrorist" had crossed the so-called Yellow Line within the Gaza Strip, behind which Israeli forces have withdrawn, and fired at Israeli soldiers.
The Israeli military claimed the attacks were against "Hamas targets" accusing the Palestinian group of opening fire towards an area where troops were operating in Gaza.
Despite the escalation, US President Donald Trump on Wednesday said that "nothing" would jeopardise the ceasefire in Gaza and added Israel "should hit back" if its soldiers were killed.
The US is seeking support from other allies, especially Gulf nations, to create an international stabilization force to be deployed to Gaza and train a Palestinian force.
