The Hamas-run health ministry in Gaza on Saturday said a 15-year-old boy was killed by IDF fire during the protest. Several of the exiled leaders attended the border protests Friday.
The delegation was welcomed by Hamas leader Ismail Haniya and members of the group's political bureau.
United Nations officials have called for the blockade to be lifted, citing deteriorating humanitarian conditions in the Palestinian enclave run by Islamist movement Hamas where 80 per cent of the two million population are dependent on aid.
An Israeli envoy has visited the Qatari capital of Doha in recent days to obtain Qatari funds for a deal to be finalized between Hamas and Israel, according to Israel's Channel 2 in a report that did not give further details.
Palestinian children play near the Gaza border with Israel (background), east of Jabalia, on August 3, 2018, as smoke billows from burning tyres and incendiary devices launched by Palestinian protesters fly in the sky.
However, Israeli Prime Minister Benjamin Netanyahu on Thursday called off a planned trip to South America and scheduled a meeting of his security Cabinet for Sunday to monitor Gaza developments.
Friday's death brought to 156 the number of Palestinians killed by Israeli fire since late March, including at least 118 in protests near the fence.
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Since the Gaza rallies began on March 30, 155 Palestinian protesters have been martyred by Israeli army gunfire.
"The delegation will arrive in Gaza for consultation over issues of concern for the Palestinian people, foremost in achieving the national reconciliation and ending the Gaza blockade", Hamas spokesman Fawzi Barhoum said.
The Israeli military said that about 8,000 Palestinians took part in Friday's rally.
The deal would purportedly include the improvement of living conditions inside Gaza, in addition to a sea port and an airport in Egypt.
Freedom was the second boat of the "Freedom Flotilla" to be intercepted en route to "break the blockade" on Gaza, the organisers said.
Critics say it amounts to collective punishment of the coastal territory's two million residents.
Earlier this week the Israeli navy intercepted a Norwegian-flagged activist boat, one of four that left Scandinavia in mid-May.