JERUSALEM — Israeli forces took control of the Rafah border crossing with Egypt on Tuesday, making their first ground incursion into the densely packed southern Gaza city where they have vowed to root out the last remnants of Hamas, an operation that angered neighboring Egypt.

An official from the Israel Defense Forces said infantry troops and an armored battalion gained “operational control” of the Palestinian side of the crossing. The official, who declined to be named in line with army protocol, said 20 militants were killed and three tunnel shafts uncovered in what he described as a “specific targeted operation” that was continuing on Tuesday morning.