Although the embassy move will take several years, Trump has directed the US State Department to "start the process".
"I would like to make a heartfelt appeal for everyone's commitment to respect the city's status, in conformity with the pertinent United Nations Resolutions", he said, as quoted by the Vatican Radio, an official broadcaster.
The pope has in the past been critical of some of Trump's policies. The call with the pontiff was made at Abbas' initiative, the Associated Press reported, citing Vatican officials.
The Vatican supports a "two-state solution" for the Holy Land with independence, recognition and secure borders for both Israel and Palestine.
Since the early 1990s, the Vatican has seen as separate issues the need for a special status for the city and questions over the political sovereignty or control of Jerusalem.
Describing the city as "holy for Jews, Christians and Muslims, who venerate the holy sites of their respective religions", the Pope said Jerusalem enjoys a unique status that should be preserved.
The former Holy See ambassador, who now serves as advisor to the Vatican's office for Integral Human Development, endorsed the appeal made by Pope Francis earlier on Wednesday to maintain the Status Quo of Jerusalem.
Pope Francis also had a discussion, regarding the moves being made by the United States, with Palestinian President Mahmoud Abbas on Tuesday.
The Pope made his comments on Wednesday during a previously scheduled meeting with a Palestinian delegation of religious and intellectual leaders.
"I pray to the Lord that this identity would be preserve and strengthened for the benefit of the Holy Land, the Middle East and the whole world and that wisdom and prudence would prevail, to avoid adding new elements of tension in a world already shaken and marked by many cruel conflicts". "We are certain that such steps will yield increased hatred, conflict, violence and suffering in Jerusalem and the Holy Land, moving us farther from the goal of unity and deeper toward destructive division", the Christian leaders wrote on 6 December.