Gaza City, Gaza Strip -- Tens of thousands of Palestinians rallied in the Gaza Strip Saturday to mark the first anniversary of their mass protests along the Israeli border, as the territory's Hamas leaders largely restrained the crowds ahead of a hoped-for cease-fire deal.

Demonstrators largely kept their distance from the border, though small crowds of activists approached the perimeter fence and threw stones and explosives toward Israeli troops on the other side. The forces responded with tear gas and opened fire, killing two Palestinians and wounding 64.

In many ways, Saturday is a test, CBS News' Seth Doane reported. The Israelis do not want to see violence escalate, particularly about a week before a key national election.

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Israeli Prime Minister Benjamin Netanyahu is seeking his fourth consecutive term in April 9 elections, but is facing a serious challenge from a group of ex-army chiefs who have criticized what they say is his failed Gaza policy. In the final stretch of the campaign, Netanyahu needs to keep the Israel-Gaza frontier quiet, without seeming to make concessions to Hamas. Netanyahu took heavy criticism this week for what was seen as a soft response to renewed rocket fire out of Gaza.

Hamas, meanwhile, faces growing unrest in Gaza as a result of worsening conditions after more than a decade of Israeli and Egyptian border closures. Hamas, which is considered a terrorist organization by Israel, is behind Saturday's protests, even bringing participants in by bus but also encouraging them to keep calm.

Protesters are crying out against what they call the siege of Gaza. Israel has sealed off the narrow Gaza Strip due to security concerns, which affects nearly every aspect of life here, from food to electricity to the ability to freely come and go. About half of Gazans are unemployed.

A Palestinian boy reacts to tear gas fired by Israeli forces during a protest at the Israel-Gaza border fence east of Gaza City March 30, 2019. MOHAMMED SALEM/REUTERS

Egyptian negotiators have been in Gaza this week trying to broker a deal that would offer to Palestinians better electricity, expanded fishing zones, fuel for power stations and foreign financial aid. In exchange, Israel is demanding Saturday's protests be non-violent and that Palestinians stop firing rockets into Israel.

Tensions increased this week after Palestinians fired a rocket into central Israel, striking a house and wounding seven. Israel pounded back with airstrikes.