The Haaretz newspaper reported that Israel's security cabinet is expected to meet on Sunday to discuss a possible deal with Hamas.
During the protests, an Israeli army tank fired a shell at a Hamas military lookout post east of Rafah in the southern Gaza Strip in response to the fire and the bomb targeting Israeli soldiers from Gaza.
Palestinian medics carry a wounded man during clashes with Israeli troops on the Gaza-Israel border, east of Gaza City, on August 3, 2018.
"We want to break the siege on Gaza once and forever", said Hussam Badran, one of the visiting Hamas leaders.
With borders to both Egypt and Israel largely sealed in recent years, Gaza suffers from desperately high rates of poverty and unemployment.
It was the second time in a week that Israel has intercepted a ship from a four-vessel flotilla heading for the blockaded Palestinian enclave.More news: Fiat Chrysler wants Mahindra Roxor to be banned in US
The March of Return demonstrations are in their 18th week against the Gaza Strip blockade by Israel and Egypt.
The deputy head of Hamas's politburo, Saleh al-Arouri, arrived in the Gaza Strip late Thursday for talks focused on the ceasefire and renewed reconciliation efforts with Fatah.
Israeli troops shot dead two Palestinians during Friday protests at the Gaza-Israel border, the health ministry in Gaza said.
Israeli Prime Minister Benjamin Netanyahu on Thursday delayed a planned visit to Colombia amid speculation that a truce agreement could be reached within days.
Israeli media said Israel was seeking a long-term commitment from Hamas to end the protests and halt the launch of the incendiary balloons and kites that have destroyed thousands of acres of farmland and forests, in exchange for lifting restrictions on the passage of goods and travel for Gaza.
On Sunday, Nickolay Mladenov, the United Nations special coordinator for the Middle East peace process, said on Twitter that he held "productive meetings" with Egyptian officials in efforts to de-escalate Gaza tensions and resolve humanitarian issues.
In a statement, Hamas spokesman Fawzi Barhoum said it included Marzouk, Rishq and Badran as well as Khalil al Hayya and Rawhi Mushtaha.