Israel's army said it had taken "operational control" of the Gaza Strip side of the Rafah border crossing with Egypt, in the south of the enclave.
The Rafah crossing, located south of Gaza City, was taken by Israeli tanks that are part of an armored brigade, the Israel Defense Forces and Palestinian officials said.
Images broadcast by the Israeli press show an Israeli flag flying on the Gaza side of the border.
The Israeli army said it had decided to take control of the crossing after receiving information that it was "being used for terrorist purposes" by the Palestinian Islamist movement Hamas, although without providing any evidence.
Israeli forces previously claimed that Hamas had used the area around the border to launch dozens of rockets that killed four Israeli soldiers near Kerem Shalom, which connects southeastern Gaza to Israeli territory.
Wael Abu Omar, the spokesman for the agency responsible for borders in the Gaza Strip government, controlled by Hamas since 2007, said that the Rafah crossing, the main entrance for humanitarian aid, was closed.
"The entire area to the west [of Rafah] has become a theater of operations since yesterday [Monday]. The shelling hasn't stopped," said Abu Omar, adding that border personnel have fled because of the Israeli offensive.
On Monday night, the Israeli army said it had killed 20 Hamas militants in "targeted attacks" in the east of Rafah, where three of the Islamist group's tunnel networks were discovered.
The Israeli War Cabinet, headed by Prime Minister Benjamin Netanyahu, announced on Monday that it had decided to continue the offensive in Rafah, while agreeing to continue negotiations for a truce with Hamas.
Israel's attack came just hours after Hamas accepted a ceasefire proposal brokered by Qatar and Egypt.
Meanwhile, the AlJazeera channel indicates that the ceasefire proposal obliges Hamas to release 33 Israeli prisoners (dead or alive), in exchange for a certain number of prisoners. In the first phase, Hamas would release all living female Israeli soldiers, also in exchange for prisoners.
In the second phase, Israel would have to leave the Gaza Strip completely.
But several signs point to the Israeli government not signing the same document - and tonight's offensive confirmed this scenario.
