Hundreds of Christians calling for the removal of the sculpture titled "McJesus" demonstrated at the museum, where the artwork has been put on display, in the northern city of Haifa last week.
Church representatives brought their grievances to the district court on Monday, demanding that it order the removal of the exhibit's most offensive items, including Barbie doll renditions of a bloodied Jesus and the Virgin Mary.
The protests appear to have been sparked by visitors sharing photos of the exhibit on social media.
Christians make up a small percentage of Israel's Arab population and say they face unique challenges.
The museum has refused to remove McJesus, however, saying doing so would infringe on freedom of expression. But following the protests, it hung a curtain over the entrance to the exhibit and posted a sign saying the art was not intended to offend.
"This is the maximum that we can do," Tal said. "If we take the art down, the next day we'll have politicians demanding we take other things down and we'll end up only with colourful pictures of flowers in the museum."
Tal's comments did little to placate those who want the artwork removed.
A protester remained camped out in a tent at the museum on Monday with a sign reading "Respect religions".
Police watched closely as local Christians complained to reporters in front of street signs spray-painted with crosses and windows still shattered from last week's clashes.
"This is very offensive and I cannot consider this art," Haifa artist and devout Christian Amir Ballan said.
"We will continue through peaceful rallies and candle vigils... We won't be quiet until we reach a solution."