The decision comes a day before the event was to occur.
The statement says that the defending Super Bowl champions disagree "with their President because he insists that they proudly stand for the National Anthem, hand on heart, in honor of the great men and women of our military and the people of our country."
A large group of Eagles players had decided not to attend, including most — if not all — of the black players, a source told ESPN's Adam Schefter.
In addressing players' decision to stay home, the president's statement said "the 1,000 fans planning to attend the event deserve better."
Trump said that he will instead have a "different type of ceremony — one that will honor our great country, pay tribute to the heroes who fight to protect it, and loudly and proudly play the National Anthem."
The team did not learn of the cancellation until the White House put out its statement, a source close to the Eagles told ESPN's Sal Paolantonio.
The source said that team owner Jeffrey Lurie was planning on attending the White House ceremony, despite some of the negative comments Lurie reportedly made about Trump in a private NFL meeting last fall. Head coach Doug Pederson and his wife, Jeannie, were also planning on making the trip, the source said.
"A lot of people in the Eagles organization are very disappointed," one league source said.
There had been ongoing conversations within the Eagles organization in the weeks leading up to the scheduled visit in an attempt to map out an itinerary that the team felt comfortable with.
In a subsequent tweet, Smith added: "There are a lot of people on the team that have plenty of different views. The men and women that wanted to go should've been able to go. It's a cowardly act to cancel the celebration because the majority of the people don't want to see you."
"I don't want to take away from anybody's experience or make it a big distraction. It's a celebratory event, and I want the guys who choose to go or whatever to enjoy that," Jenkins said in February. "Me personally, because it's not a meeting or a sit-down or anything like that, I'm just not interested in the photo op.
"Over the last two years, I've been meeting with legislators, both Republican and Democrat, it don't matter. If you want to meet to talk about events in my community, changing the country, I'm all for that. But this isn't one of those meetings, so I'll opt out of the photo opportunity."
Philadelphia mayor Jim Kenney issued a statement that said, in part, "Fans all across the country rallied behind (the Eagles) because we like to root for the underdog and we feel joy when we see the underdogs finally win. I'm equally proud of the Eagles' activism off the field. These are players who stand up for the causes they believe in and who contribute in meaningful ways to their community. They represent the diversity of our nation-a nation in which we are free to express our opinions."
Monday's decision is similar to when Trump told the Golden State Warriors last September they were not welcome at the White House to celebrate their 2017 NBA championship. In that tweet, Trump said going to the White was considered a great honor for a championship team and specifically mentioned Warriors star Stephen Curry.
Source close to the team say the team will now be expected to be at the team's training facility Tuesday in South Philadelphia to attend what is called a Phase II day of organized team activities, which includes meetings, weight training and individual on-field drills. Pederson is expected to address the media on Wednesday, when players are also expected to be available.
ESPN's Tim McManus contributed to this report.