At least 43 Palestinians have been killed and 2,200 wounded by Israeli troops, Palestinian officials say, on the deadliest day of violence since the 2014 Gaza war.
The violence came as the US opened its embassy in Jerusalem, a move that has infuriated Palestinians.
They see it as clear US backing for Israeli rule over the whole city, whose eastern part Palestinians lay claim to.
But US President Donald Trump hailed the move in a video message.
He told the dedication ceremony that it had been a "long time coming", adding: "Israel is a sovereign nation with the right to determine its own capital but for many years we failed to acknowledge the obvious."
Palestinians hurled stones and incendiary devices while the Israeli military used snipers, as black smoke poured from burning tyres.
The health ministry, run by Gaza's Islamist rulers Hamas, said children were among those killed on Monday.
The Hamas-led demonstrations are part of a six-week protest dubbed the "Great March of Return".
Israel says the protests are aimed at breaching the border and attacking Israeli communities nearby.
The Israeli military said 40,000 Palestinians had taken part in "violent riots" at 13 locations along the Gaza Strip security fence.
It said the Israeli military had killed three people trying to plant explosives near the security fence in Rafah. Aircraft and tanks had also targeted military positions belonging to Hamas in the northern Gaza Strip, it said.
There have also been violent clashes between Israeli police and protesters who raised Palestinian flags outside the new embassy. Several protesters were detained.
EU foreign policy chief Federica Mogherini has called for "utmost restraint".