The attacks followed an incident on Friday when four Palestinians and two Israeli soldiers - one of whom acted as a security co-ordinator for a nearby Israeli settlement - were killed when a crowd of Israeli settlers, some armed, approached the Palestinian village of Tal, southwest of Nablus.
During the incident, villagers came out of their homes to confront the settlers and a stand-off ensued, with video appearing to show one of the Palestinians grabbing a settler's weapon.
Palestinian local authorities say the settlers provoked the violence.
The Israeli military said shots were fired by both sides.
The incident was the latest in a series of clashes this year involving settlers in which dozens of Palestinians have been killed and hundreds wounded, according to figures from the United Nations and the Palestinian Authority.
Prime Minister Benjamin Netanyahu, facing an election in October, ordered a major security operation against what he described as terrorism against Israeli civilians, reinforcing units in the West Bank and cancelling leave.
Members of his government, including the ultranationalist finance minister Bezalel Smotrich, have called for annexation of the West Bank, territory Israel captured in the 1967 Middle East war.
Settlers carried out a series of attacks on Palestinian villages in different areas of the West Bank in the early hours of the morning, Palestinian officials said.
Abdel Azim Wadi, head of the village council in Qusra, southeast of Nablus, said settlers had torched a newly completed mosque in his village early on Sunday.
"The mosque was in its final stage and was ready to receive worshippers. It had already been furnished with couches. They set it on fire and spray-painted Hebrew slogans on its walls," he told Reuters by telephone.
Among the graffiti were messages including "Jewish revenge" and the name of one of the Israelis killed near Tal.
The Palestinian Authority, which has responsibility for the section of the West Bank where Friday's shootings took place, said the incident was part of a generalised assault on Palestinians.
"Israeli state-backed settler terrorism is intensifying into systematic pogroms across the occupied West Bank," the Palestinian prime minister's office said in a statement on X.
The Israeli military said troops sent to Qusra, which sits near several large Israeli settlements, had found graffiti and signs of arson and were searching for suspects.
It said police officers would be sent to collect evidence.
"The security forces strongly condemn incidents of this kind, including harm to religious sites, and will continue to act decisively to maintain security and public order in the area," the military said.
An Israeli military official said such violence by Israelis diverts the army's attention from its primary mission of defence and counter-terrorism in a complex environment.
The official said, though, that over the weekend troops arrested more than 130 individuals, "including weapons traffickers, Hamas terrorist operatives, individuals involved in incitement, and terrorists planning to carry out imminent attacks".
In separate incidents, Palestinian officials said settlers had also tried to burn a mosque near Kour, southeast of the city of Tulkarm, and attacked Palestinian workers at a stone-cutting facility in the town of Kafr Malik, near Ramallah.
Farid Jiyousi, a member of the Kour village council, said three settlers had tried to set the mosque ablaze at dawn but worshippers had put out the fire before it reached the mosque's main area.
"This is the first attack our village has experienced," he said, adding that the attackers had also sprayed graffiti in Hebrew on the mosque walls.
As part of a security clampdown across the West Bank over the weekend, Israeli forces arrested about 60 Palestinians from Saturday night, according to the Palestinian Prisoners Club, which tracks Palestinians in Israeli custody.
Most countries and United Nations bodies consider Israeli settlements in the West Bank illegal, a position that Israel rejects.
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