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With a White House delegation and Israeli officials set to gather for the inauguration ceremony, the Gaza clashes had wounded more than 500 Palestinians in addition to the 16 killed, the Gazan health ministry said.
The dead included a 14-year-old, according to the ministry.
Thousands had gathered near the border in protest while smaller numbers of stone-throwing Palestinians were approaching the fence and trying to break through, with Israeli snipers positioned on the other side.
Crowds built throughout the day in the Palestinian enclave less than 100 kilometres (60 miles) away from Jerusalem and sealed off from Israel by a blockade.