"Why are you apologizing all the time?" Palin asked her guides after being told Jews were not allowed to pray openly at the Temple Mount and about Arab riots that followed Prime Minister Binyamin Netanyahu's opening of an exit from its tunnels in 1996.
Israel enforces a controversial ban on prayer at the Temple Mount by non-Muslim visitors.
The Jerusalem Post, which quoted Palin asking the question, did not report what Western Wall Rabbi Shmuel Rabinovitz and conservative Israeli lawmaker Danny Danon said in response.
"She didn't go into diplomatic issues, but I can clearly say from the questions she asked in relation to our conflict here with the Muslims in these holy sites that she knows that we are right and that the Muslims are just claiming things for provocation and they're not right," the Post quoted Danon as saying.
Palin -- the subject of speculation that she may try for the Republican presidential nomination in 2012 -- described herself in a 2008 interview as a "Bible-believing Christian."
The issue of public prayer is touchy at the Temple Mount because the site is holy to both Jews and Muslims. It is known by Muslims as the Noble Sanctuary.
Traditional Judaism regards the Temple Mount as the site where God chose the "divine presence" to rest, where the world expanded into its present form and where God gathered the dust used to create the first man, Adam.
It is also where the two ancient Jewish Temples were built. The Western Wall is a remnant of an ancient wall that surrounded the Temple's courtyard and is one of the most sacred sites in Judaism outside of the Temple Mount itself.
Among Sunni Muslims, the Noble Sanctuary is considered the third-holiest site in Islam, the location of the Prophet Mohammed's journey to Jerusalem and ascent to heaven.
It is also the home of the al-Aqsa Mosque and Dome of the Rock Islamic shrine, dating from the year 691.
The dome, built when Muslims controlled Jerusalem, sits at or near where the Bible mandates the Temple be rebuilt, traditional Jews say.
"I'm so thankful to be able to be here and I'm thankful to know the Israel-American connection will grow and strengthen as the peace negotiations continue," Palin told reporters during her Sunday evening Western Wall tour.
She and her husband Todd had dinner with Netanyahu and his wife Sara at the Netanyahus' Jerusalem home Monday. The dinner was closed to the media and Netanyahu's office offered no immediate statement about it.