A rocket was launched from the Gaza Strip towards Israel just hours after the latter reopened its two main crossings with the territory, the Israeli army has said.
A projectile launched from the Gaza Strip did not cross into Israeli territory but did set off air-raid sirens in the south of the country, the Israeli army added.
There was no immediate claim of responsibility and no immediate Israeli response.
Egyptian mediators have been working in recent days to broker a ceasefire between Israel and Hamas.
The talks have been repeatedly interrupted by Palestinian rocket attacks and Israeli military reprisals. The violence comes just over a week before Israeli national elections.
Palestinian terrorists launched rockets into Israel earlier on Sunday, and the military responded with tank fire.
But Israeli and Hamas officials later confirmed that the Erez and Kerem Shalom border crossings were nonetheless opened for the first time since last Monday, when a rocket fired by Palestinian terrorists struck a home near Tel Aviv and touched off six days of hostilities.
The reopening of the crossings, which are used to allow people and cargo to move in and out of Gaza, signalled that the Egyptian efforts were making progress.
Hamas officials have said the deal would include Israel easing its blockade of Gaza in exchange for guarantees of quiet.
Four Palestinians, including three teenagers, were killed by Israeli fire on Saturday as tens of thousands of people took part in a mass rally that marked the first anniversary of demonstrations along the Israel-Gaza perimeter fence.
Dozens of activists approached the fence during Saturday’s demonstration, hurling stones and explosives toward Israeli forces.
Israel has said it is defending its border, but has come under heavy international criticism for the large number of unarmed Palestinian demonstrators who have been shot over the past 12 months.
Nearly 200 Palestinians have been killed by Israeli fire, while an Israeli soldier was killed by a Palestinian sniper last summer.