International Christian Embassy Jerusalem-USA Director Susan Michael expressed her concern that Trump was being advised to delay the efforts to move the Embassy and make it instead as part of the peace agreement between Palestinians and Israelis.
Mr Trump is also due to meet Palestinian Authority President Mahmoud Abbas in Bethlehem in the West Bank - their second meeting in the space of a month.
"People are exposed to it and it raises suspicion", he continues.
Trump was in Saudi Arabia on Saturday, the first stop of the president's first global trip, at a time when his young administration is engulfed in controversy.
While welcoming Trump's efforts and committing themselves to work with him, some Palestinian officials remain wary that he has yet to publicly back a two-state solution, the longtime bedrock of US and worldwide policy.
In recent days, United States officials have tamped down expectations of an embassy move, reportedly emphasizing to their Israeli counterparts that Trump remains committed to relocating the embassy by the end of his first term, even if he decides next month to extend the presidential order freezing the implementation of the move.
But in recent weeks the mood has since soured.
When briefing reporters on Trump's visit to Jerusalem next week, McMaster made no mention of whether Trump would make use of the visit to announce the relocation of the US Embassy from Jerusalem to Tel Aviv.
Such a decision, Arab leaders say, would inflame the Arab street and could lead to an increase in extremism. Drawing a contrast with Tillerson and breaking rank with the White House, US Ambassador to the United Nations Nikki Haley said on May 17 that Israel's capital city "should be Jerusalem", and that "the [US] embassy should be moved to Jerusalem". That distinction - Jerusalem, not Israel - reflects the US position that the city's fate is an issue for Israelis and Palestinians to work out through future peace negotiations.
Right-wing Israelis welcomed Trump's election, hopeful that he would support their vision of broader Israel. Respondents that did not know what his position was rose from 8 to 19 percent.
Hagee added, "The Jewish state has the right to determine where it would place its capital, and it has chosen Jerusalem". But the administration's preparations for the trip have tempered Israeli excitement around his visit.
Trump administration officials have questioned whether Israel's Western Wall area, one of Judaism's most holy sites, is actually part of Israel.
Trump will be the first sitting US president to visit the site, although Barack Obama and George W. Bush did so either as candidates or private citizens.
While Israelis and Palestinians alike are uncertain what Trump will ask of them, experts believe he will be looking to coax them to make an explicit commitment to return to the table without pre-conditions, start work on a timetable for talks and consider mutual "confidence-building" steps. Just nine percent of Palestinians believe Trump's actions will lead to a renewal of the peace process.