The law also will allow for the state to deport anyone whose residency status has been withdrawn.
Roman Catholic officials issued a statement saying that Christian leaders were holding consultations and would soon announce their response, including a decision on whether to reopen the Church of the Holy Sepulchre.
The number of Jewish settlers in the West Bank grew at nearly twice the rate of Israel's overall population last year.
Pence was in Jerusalem on Monday, expressing his full-throated support for Israel in a speech to parliament filled with biblical references.
Bishop Elizondo was among 10 Hispanic U.S. bishops visiting the Holy Land to advocate for "bridges not walls."
Sheik Ahmad el-Tayeb, the grand imam, hosted a meeting Jan. 17-18 with Christian and Muslim clerics and political leaders from 86 countries in reaction to President Trump's decision to recognize Jerusalem as the capital of Israel.