With the Patriots lined up behind him, Trump said: 'No team has been this good for this long'.
Super Bowl champion players often miss the annual White House victory visit due to scheduling conflicts.
Branch is among numerous Patriots players who opted out of the visit for various personal and political reasons.
Trump did not mention Super Bowl MVP Tom Brady, who did not attend the ceremony after announcing Wednesday he would not go because of family matters.
Before the ceremony, star tight end Rob Gronkowski tried to inject some levity by crashing White House press secretary Sean Spicer's daily media briefing.
Also not addressed in the ceremony was the morning news of former Patriots player Aaron Hernandez's suicide. As was the case in those years, the thinking was that the number of players present was reduced in part because for some who were invited the novelty of going to the White House wasn't the same as it was two years ago.
A team spokesman said the Patriots were aware of situation, but neither the team or Trump publicly addressed the news surrounding Hernandez.
Alan Branch initially told reporters he would be staying to spend time with his family, but revealed to the Boston Globehe chose to stay because of sexist remarks made in the past by the president.
A website about the march Bündchen linked to, which will take place April 29 in D.C., says the event falls on the 100th day of the Trump administration.
"Need some help", Gronkowski asked to a chorus of laughter. Hernandez was found by guards in his cell at a MA correctional facility.
"Thank you to the President for hosting this honorary celebration and for supporting our team for as long as I can remember", Tom Brady said in a statement.
Brady's mother has also reportedly been suffering from health problems.
The 27-year-old Hernandez was serving a life sentence for the 2013 shooting death of a friend. Hopefully, if we accomplish the goal of winning a championship in future years, we will be back on the South Lawn again soon. "With the president having so many strong opinions and prejudices, I believe certain people might feel accepted there while others won't".
"What a great day it is to be with all of our friends at the White House".