JERUSALEM — Israeli ground forces crossed into southern Lebanon early Tuesday, marking a significant escalation of an offensive against Hezbollah militants and opening a new front in a yearlong war against its Iranian-backed adversaries. The incursion follows weeks of heavy blows by Israel against Hezbollah—including an airstrike that killed its longtime leader, Hassan Nasrallah—and seeks to step up the pressure on the group, which began firing rockets into northern Israel after the start of the war in Gaza.