Two Israelis entered the Church of Gethsemane and attempted to damage items inside, according to a report by the Palestinian news agency Wafa.
A Palestinian man at the scene stopped them.
The attempted attack came after two Israeli radicals defaced a Christian cemetery in East Jerusalem on New Year's Day. The attackers toppled tombstones and smashed crosses located at the Protestant cemetery.
"It really grieves us to see what happened over the New Year holiday when we discovered that more than 30 tombstones and crosses were smashed to pieces by at least two Jewish extremists," Anglican bishop Husam Naoum said at the time.
"I ask for action to be taken; the perpetrators brought to the law and be a lesson for others."
The bishop attributed the attack to increased hate speech within Israeli society.
Palestinians in Jerusalem experience frequent violence from Israeli settlers and forces and both Christian and Muslim holy places come under attack.
The Al-Aqsa Mosque compound, which is the third-holiest site in Islam and the most-sacred Muslim place in Palestine, often faces raids.
Israeli extremists commonly enter the site under the protection of Israeli forces as they worship in violation of the longstanding status quo arrangement in place there.
Violence against Palestinians at the compound often skyrockets during the Muslim holy month of Ramadan, which this year will begin later in March.
Israeli forces' actions at Al-Aqsa during Ramadan 2021 were central to sparking an 11-day escalation in Gaza that saw more than 250 Palestinians killed by Israeli bombardment of the besieged coastal strip.