Israeli troops have killed two Palestinians in separate incidents when they opened fire near the border in the Gaza Strip, medical officials have said.

Ashraf al-Qudra, a spokesman for Gaza's emergency services, confirmed a man in his early 20s was shot dead by troops near the northern border, but said they had not yet been able to retrieve his body.

A spokeswoman for the Israeli military said troops had opened fire on an armed Palestinian, saying he had fired at them first.

"A Palestinian opened fire at Israeli troops not far from the security barrier separating Israel from the northern Gaza Strip, and they responded by firing in his direction," she said.

In an unconnected incident earlier on Friday, Israeli border police killed a man and wounded another who had tried to cross the Egyptian border into Israel.

An Israeli security source said they were both unarmed Gazans.

"Overnight, Israeli border police identified two suspects infiltrating Israel through the Israel-Egypt border," an army spokesman said.

"In accordance with the rules of engagement, the border police sought to stop the infiltration and fired at the suspects. Upon the arrival of Israeli army medics, one of the suspects was pronounced dead," he said.

The second was taken to hospital.

The military spokesman noted that "illegal infiltrations through the Egyptian border are used by terror organisations to execute terror attacks against Israeli civilians and security forces".

He said the incident took place in the middle of Israel's 240-kilometre border with the Egyptian Sinai.

On Thursday, Israeli armed forces killed a Palestinian fighter and wounded another two in a drone airstrike.

In the earlier incident, three men who were travelling in a car in Shejaiya, a neighbourhood in the east of Gaza City, were injured when a tank shell struck their vehicle and another landed nearby, medics said.

One of them was critically wounded, while the other two were moderately hurt.

(Agencies via Al Jazeera)