The statement went on to thank the President for the honorary celebration and for supporting the team.
Press secretary Sean Spicer's briefing had been going on for about 20 minutes when the tight end opened a door and poked his head around the corner of the dais.
The Patriots are at the White House to meet President Trump and attend a ceremony honoring the team's Super Bowl LI win. Several players explicitly cited their opposition to Trump as their reason for not attending.
Trump hyped his relationship with Patriots quarterback Tom Brady and coach Bill Belichick during the presidential campaign.
President Trump's welcome to the team was coming hours after the news from MA prisons officials that ex-Patriot tight end Aaron Hernandez hanged himself in his prison cell.
Brady, who faced controversy during the 2016 election when a "Make America Great Again" hat was spotted in his locker, has been evasive when asked about Trump, keeping his comments non-political.
Should the Patriots decline to match, the defending Super Bowl champion would receive a first-round pick compensation from Malcolm Butler's new team.
There were other reasons for player absences, however.
Wide receiver Malcolm Mitchell said he was moved by the White House ceremony, saying it "almost brought me to tears. With the president having so many strong opinions and prejudices I believe certain people might feel accepted there while others won't".
The president addressed the Patriots players, coaches and owner Robert Kraft on the South Lawn in recognition of their thrilling comeback win in which they overcame a 28-3 deficit to push the game into overtime and take home another Lombardi Trophy. "... This year's championship was achieved after falling behind by 25 points, a deficit so great that in the 97-year history of the National Football League, over 20,000 games, that deficit had only been overcome seven times".
Noting "pundits" had given the Patriots up for dead in February's Super Bowl against the Atlanta Falcons, only to watch them clinch a last-minute victory, Trump quipped: "Good old pundits, boy, they are wrong a lot, aren't they?"
Presidents for years have invited sports figures to the White House, but the tradition of honoring championships teams there solidified under Ronald Reagan. That includes Brady in 2015.