In his first such event since causing an uproar last week with remarks about a white nationalist demonstration in Virginia, Trump was expected to make remarks at the rally but not use the event to pardon former Sheriff Joe Arpaio.
Phoenix Mayor Greg Stanton, a Democrat, had asked Trump to postpone Tuesday's event scheduled for 7 p.m. MST (0200 GMT on Wednesday).
Neither John McCain nor Jeff Flake, the state's senators, was expected to attend, said a source familiar with the Flake campaign and published reports, underscoring Trump's fractious relationship with some in his own party.
Republican Governor Doug Ducey told the Arizona Republic on Monday that he would welcome Trump on the tarmac when he arrived but would not attend the Phoenix rally.
The president had earlier held out the possibility of a pardon for Arpaio, a former sheriff of Maricopa County and an outspoken opponent of illegal immigration.
Arpaio, 85, was found guilty last month of criminal contempt for violating the terms of a 2011 court order in a racial profiling case. He lost a re-election bid last year.
But White House spokeswoman Sarah Sanders told reporters traveling with Trump on Air Force One: "There will be no discussion of that today at any point and no action will be taken on that front at any point today."
Before flying to Phoenix, the state capital, Trump landed in Yuma, Arizona, near the Mexican border, for a tour of border security facilities there. He is seeking congressional funding for a wall he wants built along the border..
HEAVY POLICE PRESENCE
Hundreds of Trump supporters lined up for hours to attend the rally in Phoenix, chanting: “Build the wall." There was a heavy police presence around the venue, with officers deployed between the crowd awaiting entry and few dozen protesters on the other side of the street. Thousands of protesters were expected to arrive later.
Trump was widely criticized for blaming both white nationalists and counter-protesters for the deadly violence at a rally earlier this month in Charlottesville, Virginia, that was organized by neo-Nazis and white supremacists.
Some White House officials privately expressed concern on Monday about Trump's Phoenix rally, fearing he might revisit the Charlottesville issue in the heat of the moment while cheered on by thousands of supporters.
"The president is always welcome in Arizona," Flake spokesman Will Allison said in an emailed statement.
Flake "hopes the president will speak constructively about moving forward with tax reform, border security, and other important issues facing our country," Allison said.
Earlier this summer Flake, 54, published a book questioning the direction of the Republican Party in the Trump era, making him one of the few party members willing to criticize the president.
Last week, Trump sent a tweet voicing support for Flake's challenger, Kelli Ward, in next year's Arizona Senate Republican primary. In the tweet, Trump called Flake "toxic" and "weak."
Michael Steel, a Republican strategist who was a senior aide to former Republican U.S. House of Representatives Speaker John Boehner, said: "Senator Flake is a popular and principled conservative voice in the United States Senate. Attacking him is stupid and counterproductive.
"Instead, the president should be focused on expanding the Republican majority by targeting obstructionist Senate Democrats, especially the ones in states he won last year."
The president has also made caustic remarks about McCain, the former Republican presidential nominee and war hero. A spokesman for McCain could not immediately be reached.
The Phoenix event will be Trump's first trip as president to Arizona, which he won in the 2016 election.
Banner/Thumbnail Credit: REUTERS/Darrin Zammit Lupi