Four Palestinians were killed on Saturday, Gaza medical officials said.
But Saturday's rally was smaller than expected, despite concerns that the anniversary would see a major escalation.
Saleh Higazi, the deputy director of Amnesty for the Middle East and North Africa, said that the dimension and nature of wounds inflicted to Gaza demonstrators by Israeli forces "induce us to think that Israel adopted a deliberate strategy to mutilate civilians".
Gaza health officials claimed three Palestinians were killed during this weekend's riots.
Israel rejects any such return, saying that would eliminate its Jewish majority. There was also less acrid black smoke swirling around with little sign of tyre-burning, as on previous weekends.
The Israeli military estimated 40,000 Palestinians were gathered at the marches. Al-Shawa was due to get married in two weeks, but an Israeli airstrike on a Gaza City building destroyed his sister's apartment, where he had rented a second floor bedroom and had amassed everything he and his bride needed for the wedding.
Saturday's demonstrations will mark the anniversary of Land Day, a day expressing solidarity with the Palestinians. As a result of the demonstrations, one member of the Israeli security forces was killed and six others were injured. My father is unemployed so I will be unable to go to university.
Israel deployed several thousand troops along the border, with the anniversary coming at a sensitive time ahead of its April 9 elections.
Protest organisers say the weekly event will continue into a second year, and proposed one for next Friday.
Prime Minister Benjamin Netanyahu said on Tuesday he was prepared for further military action in Gaza after cutting short a Washington visit and returning to Israel following a shaky ceasefire announced by Hamas.
The veteran Israeli leader faces a serious challenge from a centrist party led by a former general and pressure from hawkish allies in his right-wing coalition to be tough on security.
Israel bolstered its forces around the enclave in advance.
The "Great March of Return" demonstrations are occurring against the backdrop of an unprecedented humanitarian crisis facing the Gaza Strip, negatively affecting the livelihoods and access to essential services of two million residents, 70 per cent of whom are Palestine refugees.
Hamas officials say an understanding was reached that would see Israel ease its crippling blockade of Gaza in exchange for the protests remaining calm.
The Israeli Foreign Ministry said on Friday that Hamas had fired 1,233 rockets from Gaza in the past year, set off 94 explosive devices and set fire to more than 8,000 acres of Israeli land.
Since Hamas seized control of Gaza by force in 2007, it has fought three devastating wars with Israel.