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The organisers of Gaza's Great Return March demonstrations reportedly moved the protest's sit-in tents closer to the Israeli border fence on Thursday, a day before a fourth planned mass demonstration, in a bold move amid fears of more bloodshed.

The protests, marking 70 years of forced displacement since the 1948 Nakba, began on March 30. Organisers have said they intend to gradually move the camps toward the fence until May 15, but made conflicting comments about a possible breach.

Hamas says the protests are aimed at ending the crippling border blockade that was imposed by Israel and Egypt after the Islamic militant group overran the territory in 2007 - a year after winning Palestinian parliament elections.

However, thousands of Palestinian women and children are participating in the marches and tent protests in a call to recognise the right of return of the descendants of some 700,000 Palestinians who fled or were forced from homes in the 1948 war over Israel's creation.

The majority of such demonstrations have been peaceful, sparking outrage when dozens of protestors were killed and over 1,500 injured by live ammunition alone, fired by hundreds of Israeli snipers stationed at the border.

Hamas and representatives of other militant factions have however voiced that a border breach is being considered.

"We will cross the border," said Daoud Shehab, a member of the organising committee from the smaller Islamic Jihad group, adding that Israel "should feel really jittery as a result of these marches."

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Israeli military officials have warned that they will "not tolerate" a mass border breach or permit protesters to get close to the fence. Earlier this week the military carried out an incursion into Gaza territory to lay more barbed wire along the already heavily fortified border area.

Israel's military also said on Thursday that it is "ready for all scenarios" and is "prepared to prevent any breach of Israeli sovereignty or damage to the border fence."

In the past three weeks, Israeli troops firing from across the border fence have killed 33 protesters and wounded more than 4,000.

Rights groups have branded Israel's open-fire regulations as unlawful, saying they permit soldiers to use lethal force against unarmed protesters.

In the past three weeks, Israeli troops firing from across the border fence have killed 33 protesters and wounded more than 4,000, according to Gaza health officials.

Among those killed was a man praying, a bystander, and journalist Yasser Murtaja, who was shot despite wearing a clearly marked "press" flak jacket.

Read more: Right of return must be at the heart of Palestinians' struggle

During the weekly Friday marches, most protesters have remained in the five sit-in tent camps, but smaller groups have moved toward the fence, throwing stones and burning tyres.

On Thursday, organisers moved tent camps several dozen metres closer to the fence, AP reported.

In a camp east of Gaza City, five tents were moved to within 300 meters (328 yards) of the border, just in range of tear gas volleys.

Bulldozers also raised protective sand berms around the new tents. In another protest site in southeastern Gaza, earth mounds were created to define the camp's new boundary.

Thursday's development came as tens of thousands of Palestinian citizens of Israel held another mass protest marking the Great Return March, which coincided with Israel celebrating 70 years since the Jewish state was established.

Palestinians have long claimed the right to return to homes or locations they were forced out of in 1948. Israel has rejected the demand.

Agencies contributed to this report.