Both incidents occurred in the Hebron area with tensions running high ahead of the Yom Kippur and Eid al-Adha 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 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.
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Separately today 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.
A string of incidents between the army and Palestinians in the Hebron area had also occurred yesterday, 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.
The Muslim Eid al-Adha holiday begins tomorrow evening and continues until Sunday.
Israel has deployed thousands of police in Jerusalem and is closing it off from the West Bank.