Israeli troops and armored vehicles crossed into southern Gaza early Wednesday in what the Israeli military said was an attempt to rescue a soldier kidnapped by Palestinian militants. Soldiers backed by artillery traveled from the Israeli military encampment in Kerem Shalom to the southern Gaza town of Rafah, near the Gaza-Israel-Egypt border, said the Israeli Defense Ministry. The Israelis took up positions in Gaza shortly before 3 a.m. (8 p.m. ET) in the area where Cpl. Gilad Shalit was abducted Sunday. Two other Israeli soldiers were killed in the weekend raid by Palestinian militants who tunneled into Israel. "The IDF will continue to act with determination and to employ all means at its disposal to combat terrorists and their infrastructure ... and will continue to make every effort to return Cpl. Shalit home quickly and safely," the Israeli military said Wednesday in a statement. "The Palestinian Authority, led by the democratically elected Hamas government, is fully responsible for any attacks emanating from the Gaza Strip, and Israel holds it responsible for the safe and quick return of Cpl. Shalit." Before Wednesday's incursion began, two rounds of Israeli airstrikes knocked out a power plant in Gaza City, cutting power to most of the territory. Video from the Palestinian Ramattan news agency showed fires burning at the site. Two bridges in central Gaza were hit in order to restrict the movement of the militants holding Shalit, said Capt. Jacob Dallal, a military spokesman. "We are trying to make it clear to the Palestinian Authority and to the terror organizations that we will take the necessary steps to secure his safe return," Dallal said. Another airstrike knocked out a bridge connecting the northern and southern districts of Gaza City, witnesses told CNN. Later, the Israelis struck one of the three bridges again.