Palestinians have gathered for protests along the Gaza Strip's border at least weekly since March 30.
At least 39 rockets have been fired at southern Israel by the Islamic Jihad group since late yesterday, with 17 of them intercepted by the Iron Dome air defence system, and the rest hitting open fields, the army said.
The air strikes came after five Palestinians were killed and 170 others wounded by Israeli troops during demonstrations along Gaza-Israel buffer zone..
"We will abide by the cease-fire if the enemy does the same", the Gaza-based militant group said in a statement, while also vowing to "protect the resistance and its position that if attacked will respond to blood with blood".
Israel has come under heavy worldwide criticism for what many see as excessive use of force and the large number of unarmed people who have been shot.
Hamas, an Islamic militant group sworn to Israel's destruction, had previously scaled down the protests as Egypt stepped up its efforts to secure calm.
Israel and Hamas have fought three wars since 2008, and Egypt and the United Nations have been leading diplomatic efforts to avert a fourth.
Although Islamic Jihad often acts independently of Hamas, Israel holds Hamas, which has ruled Gaza since 2007, responsible for all fire emanating from the territory.
A fifth died when a hand grenade he was holding exploded accidentally, witnesses said.
According to the Palestinian Health Ministry, 213 Gazans have been killed by Israeli forces during the protests.
While Greenblatt is expected to meet with Israeli Prime Minister Benjamin Netanyahu, it remains unlikely that there will be a sit-down with Palestinian Authority President Mahmoud Abbas, who has maintained an administration-wide boycott of the Trump team since the president recognized that Israel's capital is Jerusalem and subsequently moved the US' embassy there.
Thousands of Palestinian demonstrators have come out for 31 weeks to denounce the blockade of the Gaza Strip and call for the right of return of Palestinian refugees to the homes, from which they and their families were displaced during the establishment of the state of Israel. Israeli media said that six people had been minorly injured during the rocket attacks.
The London-based Arabic newspaper Al-Hayat reported Friday that a deal had been reached that would see the protests end in exchange for an easing of Israel's blockade. In response the Israeli army carried out air strikes on around 20 Hamas targets in Gaza.
Hamas officials denied a deal had been struck but confirmed to AFP that progress was being made.
Egyptian security officials have been talking separately to Israeli and Palestinian leaders in an attempt to restore calm along the border.
Gaza militants fired a barrage of rockets into Israel on Friday evening, triggering red-alert sirens across the Gaza periphery into the early morning hours.
Israel says its 11-year blockade is necessary to isolate Hamas, while critics say it amounts to collective punishment of Gaza's two million residents.