Israel says it has closed the Erez crossing after it came under rocket fire from Gaza, wounding four people, BBC reported.
The crossing is used by aid workers, journalists and Palestinians with Israeli permits to enter or leave Gaza.
Meanwhile, an Israeli air strike in northern Gaza killed a mother and three children, local health officials said.
More than 2,090 Palestinians - mostly civilians - and 67 Israelis have died in recent fighting between Israel and Palestinian militants.
Most of the dead on the Israeli side have been soldiers. A Thai national in the country was also killed by rocket fire early on in the six-week-old conflict.
Hostilities between the two sides resumed on Tuesday after a temporary truce, scuppering efforts by Egyptian negotiators to achieve a long-term ceasefire deal.
Hamas finance chief 'killed'
The Israel Defence Forces (IDF) said Palestinian militants had fired missiles at the Erez crossing from a concealed rocket launcher in northern Gaza.
The military added that at least 50 missiles had been fired into Israel since Saturday night.
It said Israeli forces were continuing their air strikes targeting sites of Hamas, the militant group which dominates Gaza.
One of the raids killed Mohamed al-Oul who was in charge of managing Hamas' funds, according to the IDF. Hamas has not yet commented on the alleged killing.
Meanwhile, Gazan health officials said a mother and three children died when their home was bombed near the Jabaliya refugee camp.
Sunday's fighting has claimed at least eight lives in Gaza.
The previous day, 22 people were hurt when a 12-storey block - said by Israel to be a Hamas command centre - was demolished by two missiles.
Israeli Prime Minister Benjamin Netanyahu has once again warned Palestinian civilians to evacuate "from every site from which Hamas is carrying out terrorist activity".
"Every one of these places is a target for us," he said in a cabinet meeting on Sunday.
Israel had announced it would "intensify" its offensive after a four-year-old Israeli boy was killed in a village near the Gaza border.
In an interview with Yahoo News, Hamas leader Khaled Meshaal rejected the charge that his organisation was targeting Israeli civilians.
"We try most of the time to aim at military targets and Israeli bases," Mr Meshaal said. "But we do not have the weapons available to our enemy… so aiming is difficult."
The current fighting erupted after tensions soared with the killings of three Israeli teenagers by Palestinian suspects in the West Bank in June, followed by the murder of a Palestinian teenager in Jerusalem in an alleged revenge attack by Jewish suspects.
Palestinian President Mahmoud Abbas earlier called on Israel and Hamas to attend fresh talks in Egypt.
Mr Abbas, who controls the West Bank, formed a unity government with Hamas in April, prompting Israel to freeze peace talks.
The Israeli government has vowed to pursue its military campaign until "full security" is achieved through the disarmament of Hamas and other groups in Gaza.
Hamas has insisted on a lifting of the economic blockade of Gaza as part of any longer-term deal.
Bakudaily.Az
