Israeli authorities intercept illicit goods heading for Hamas on a regular basis at crossings from Israel into the Strip.
The new rounds of dialogue will be the first since the two group's meetings held in Qatar in 2016.
Delegates from Hamas and rival group Fatah are due to meet in Cairo on Tuesday as part of Egyptian efforts to achieve inter-Palestinian reconciliation and allow the West Bank-based unity government to assume its responsibilities in the Gaza Strip.
Two Palestinian delegations, representing Palestinian President Mahmoud Abbas Fatah Party and Islamic Hamas movement left on Monday for Cairo to conduct a reconciliation dialogue, which aims at ending more than ten years of internal split.
Security sources in Rafah town said the four, including Eassa were arrested at a security forces checkpoint in Rafah town. "The effect is that we basically trust them to take steps that restrain Hamas and undermine their legitimacy in the long run". "Any money entering Gaza should go through it".
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What should be raised in the talks is the "enhancement" of Hamas' power and all the subjects that are "obstructing the reconciliation", he added.
Israeli commentators were divided on whether Hamas's move represents a victory or a setback for the movement.
In 2006, Hamas swept the Palestinian legislative elections, clenching 44.5 percent of the vote and securing 74 seats in the Palestinian Legislative Council.
"The contentious issues with Fatah were agreed upon during 2011 in Cairo", Yahya Moussa, a Hamas leader, told Al-Monitor.
"Today, we stand before an important historic moment as we begin to get over our wounds, put our differences aside and place the higher national interest above all else", he said at the televised meeting. He spoke on condition of anonymity pending an official announcement.