Both incidents occurred in the Hebron area with tensions running high ahead of the Yom Kippur and Eidul Azha holidays and after three days of clashes rocked Jerusalem's Al-Aqsa mosque compound last week.
An Israeli army spokeswoman said the Palestinian man was killed by an explosive device he intended to toss at a military vehicle. Residents provided a similar account.
Palestinian security officials however said he was shot dead by Israeli troops in the village of Dura near Hebron. They named him as Dia al-Talahmeh, 21.
The army spokeswoman said a patrol had been deployed to clear stones blocking a road outside Hebron.
"The soldiers heard an explosion and during a search of the sector they found the body of a Palestinian killed by the explosive device he intended to throw at one of our vehicles," she said.
Separately on Tuesday morning, Israeli troops shot and wounded a Palestinian woman at a checkpoint near the centre of Hebron, witnesses said. The Israeli military said she had attempted to stab a soldier.
"An attack was thwarted when a Palestinian attempted to stab an (Israeli) soldier at a military position in Hebron," an army statement said.
"(Israeli) forces responded, fired towards the perpetrator and identified a hit."
A string of incidents between the army and Palestinians in the Hebron area had also occurred during the day on Monday, residents said.
Tensions have been running high across the West Bank, including Israeli-annexed east Jerusalem, ahead of the Jewish Yom Kippur holiday which begins at sundown on Tuesday.
The Muslim Eidul Azha holiday begins on Wednesday evening and continues until Sunday.
Israel has deployed thousands of police in Jerusalem and is closing it off from the West Bank.
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