Israel launched its ground assault into Rafah on May 6, causing around 1 million Palestinians to flee the city.
Friday's statement by the Israeli military suggested its forces have been operating in most parts of the city.
In the first few weeks the Israeli assault focused on in Rafah's eastern districts and in areas close to the border with Egypt.
Israeli troops seized the Rafah crossing into Egypt on the first day of the offensive and have since claimed control over the Philadelphi Corridor, a road running the length of the Gaza-Egypt border on the Gazan side.
Earlier this week, Israeli troops also moved into Rafah's western district of Tel al-Sultan, where heavy clashes with Hamas fighters have been reported by witnesses.
In its statement Friday, the military said its troops in central Rafah had uncovered Hamas rocket launchers and tunnels and dismantled a weapons storage city of the group.
It did not specify where in central Rafah the operations were taking place, but previous statements and witness reports have pointed to raids in the Shaboura refugee camp and other sites near the city centre.
Israel has said an offensive in Rafah is vital to uprooting Hamas fighters in its military's campaign to destroy the group after its October 7 attack on southern Israel.
Palestinians who fled the city have scattered around southern and central Gaza, most of them living in squalid tent camps.
Up to around 300,000 people are believed to remain in the area, some of them still in the central urban parts of the city, a U.N. official said.
Shaina Low, a spokesperson for the Norwegian Refugee Council, a humanitarian group that operates in the area, said most have flocked to a rural area west of the city near the coast — an area that has seen deadly Israeli strikes and shelling the past week.
More than 1 million Palestinians have fled the city since the assault began.
