At least 40 Palestinians were shot by Israeli fire in the protests, Gaza’s health ministry said, with volunteer medic Abdullah al-Qatati killed after being hit in the chest east of Rafah in southern Gaza.
A 55-year-old Palestinian, Ali al-Alul, was killed by Israeli fire on the same stretch of the border.
A few thousand protesters had gathered in different locations along the border with Israel, setting tyres ablaze and throwing stones, but there were fewer people demonstrating that in previous weeks, AFP correspondents said.
The Israeli army said a grenade had been thrown at troops in northern Gaza which did not injury any soldiers.
“In response to the violent riots, IDF (army) tanks struck two Hamas posts in the northern Gaza Strip,” the military said on Twitter.
The protests came after a deal to end all rocket fire into Israel and air strikes on the Gaza Strip appeared to go into effect around midnight (2100 GMT) on Thursday.
There was no official confirmation from Israel or Gaza’s Islamist rulers Hamas but there were no fresh strikes Friday.
Thursday had seen extensive Israeli raids in retaliation for the launching of more than 180 rockets and mortar rounds by Hamas and its allies on Wednesday night.
Three Palestinians were killed in the Israeli strikes, including a pregnant woman and her 18-month-old daughter, while seven Israelis were wounded by Palestinian rocket fire as hundreds took refuge in bomb shelters.
The European Union on Friday said “the death of the pregnant Palestinian mother and her child in this latest escalation is a tragic loss”.
It was one of the most serious flareups since the 2014 Gaza war and followed months of escalating tensions.
‘Dangerously close’ to conflict
Late on Thursday, an Israeli air raid flattened a five-storey building which hosted a cultural centre in Gaza City but which the army said was used by Hamas security forces.
The Israeli security cabinet and the Hamas leadership met separately on Thursday, with the truce offer brokered by Egypt and the United Nations on the table.
Neither Israel nor Hamas officially confirmed any truce had gone into effect, although that has also been the case with previous informal arrangements.
It would be the third such truce in a month.
Reserve General Doron Almog, former head of Israel’s southern command which deals with Gaza, told army radio on Friday morning that the next 24 hours would be crucial.
“We are closer to an arrangement than we have been in the past because Hamas’s interest in a deal is greater than its wish for escalation,” he said.
The European Union said Gaza and Israel are “dangerously close” to a new conflict, calling for urgent “de-escalation” to keep civilians from further risk.
Hamas and Israel have fought three wars since 2008.
The Israeli daily Maariv wrote that during the security cabinet meeting on Thursday Defence Minister Avigdor Lieberman was a lone voice in support of a new war in Gaza.
“He was the only one who demanded to launch a large-scale operation in the Gaza Strip. Netanyahu was opposed. The (Israeli army) also didn’t recommend it,” he said.
Hugh Lovatt, Israel-Palestine fellow with the European Council on Foreign Relations, said the “increasingly frequent cycles of escalation and de-escalation” were similar to events before the previous wars.
“Unlike the run-up to past wars, there is already a sustained diplomatic push to hammer out a ceasefire,” he told AFP.
“Yet their ability to avoid renewed war is becoming increasingly constrained with each cycle of violence,” Lovatt added.
Palestinians have been protesting along the Gaza-Israel border on Fridays since late March.
They are calling for an end to the decade-long Israeli blockade of Gaza and the return of Palestinian refugees to their ancestral homes inside Israel, which they fled or were expelled from during the war surrounding Israel’s creation in 1948.
Israel says its blockade is necessary to isolate Hamas, although critics say it amounts to collective punishment of Gaza’s two million residents.
It says any significant return of refugees would mean the end of it as a Jewish state.
At least 167 Palestinians have been killed since protests began on March 30.
Most were killed by Israeli fire during the protests but others died in air strikes.
One Israeli soldier was shot dead by a Palestinian sniper.