Amjad Gundi, a 20-year-old man from the West Bank village of Yatta, stabbed a soldier and tried to take his weapon in the town of Kiryat Gat before being shot dead by police, a spokesman said.
Earlier, a Palestinian woman stabbed an Israeli man who then shot and wounded her in Jerusalem’s Old City.
The incidents come amid an upsurge of violence in Israel and the West Bank.
Israeli Prime Minister Benjamin Netanyahu has postponed until further notice a trip to Germany planned for Thursday, citing the security situation.
Israeli police spokesman Micky Rosenfeld said Amjad Gundi approached the Israeli soldier after stepping off a bus in Kiryat Gat and managed to snatch his weapon in a struggle that left the soldier with light injuries.
The man then fled into a residential building, where police forces tracked him down and shot him dead, Mr Rosenfeld added.
An ambulance service spokesperson earlier said in a statement that two people had been lightly wounded and taken to hospital in the city of Ashkelon.
In the Jerusalem attack, an Israeli man in his 30s was stabbed from behind in his upper body, sustaining moderate injuries, an Israeli police spokesperson said.
The man then drew his personal weapon and shot the 18-year-old female assailant from Sur Baher in East Jerusalem, who was taken to hospital in a serious condition, they added.
The attack came after Israeli authorities lifted some of the tight security measures put in place following a series of deadly attacks.
On Saturday, a Palestinian stabbed two Israelis to death in Jerusalem’s Old City. Another Palestinian stabbed and wounded an Israeli teenager elsewhere in the city. Israeli police killed both attackers.
And last Thursday, gunmen shot and killed an Israeli couple as they drove with their four young children in the West Bank. Israeli police say five members of the Palestinian militant group Hamas have confessed to the shooting.
Meanwhile, Israeli forces shot dead two Palestinian youths during clashes with protesters in the West Bank on Monday. Israeli media quoted military officials on Tuesday as saying one of them, a 13-year-old boy, had been shot by mistake.