The change in the President's pronunciation seemed particularly to affect "s" and "th" sounds, and appeared to worsen in the closing stages of the address.
It led viewers to suggest the President may have suffered a medical problem.
The 71-year-old did not appear otherwise impaired and following the speech immediately moved over to a table and signed a declaration.
A White House official told CNN Mr Trump was "perfectly healthy".
They added: "He's been working in meetings all day and in fact is still here working now."
In the footage Mr Trump can be seen adjusting his mouth a number of times.
Speech pathologist Michael de Riesthal told the broadcaster the US leader was "working hard to speak" as though he was "having a denture fall or some other alternative explanation".
While Mr Trump completed the majority of his address without any noticeable divergence from his normal speech patterns, footage appears to show him making the adjustments from about four minutes in.
His deputy press secretary, Raj Shah, told The Los Angeles Times: "His throat was dry. There’s nothing to it."