He was expected to meet with Israeli Prime Minister Benjamin Netanyahu on Monday afternoon before a private dinner with spouses at Mr Netanyahu's Jerusalem residence.
Ynet News reported a senior American official saying that "the USA is discouraging actions that it believes will unduly distract the principals from focusing on the advancement of peace negotiations".
The law stops short of annexing West Bank territory to Israel, and its practical implications are unclear.
The statement came hours after coalition chairman David Bitan (Likud) told Army Radio a vote on the "Greater Jerusalem" bill in the key Ministerial Committee for Legislation on Sunday was delayed because "there is American pressure claiming this is annexation".
The Greater Jerusalem legislation would bring some Jewish settlements built in the Palestinian West Bank under the jurisdiction of Jerusalem's municipal authority.
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The official confirmed a meeting on Sunday in Jerusalem between Jason Greenblatt. It was a signal that Netanyahu was under pressure not to move forward from the White House, which has been seeking ways to restart long-stalled Israeli-Palestinian peace talks. We have to take the time to clarify matters to the Americans. But in the occupied West Bank, anger is continuing over illegal Israeli settlements.
The worldwide community is widely opposed to settlement construction. The bill has drawn harsh criticism from Palestinians and those hoping to salvage the two-state solution.
Netanyahu had previously indicated that he would give his backing for the proposal to absorb Ma'ale Adumim, Beitar Illit and Efrat, along with the Etzion bloc of settlements, into the Jerusalem municipality.
Intelligence and Transportation Minister Yisrael Katz, who has pushed for the bill, says it would add an additional 150,000 people to Jerusalem's population, strengthening its Jewish majority. However, it has not received recognition of its claim by the global community and most embassies, including that of the U.S., are still in Tel Aviv. His ambassador to Israel, David Friedman, is himself a supporter of Israeli settlements.