One could say:
He speaks with a strong Southern dialect.
If you are in the United States, one would picture a Texan. However, that same sentence said in Britain would mean he speaks like Hugh Grant.
If someone says:
He speaks with a Southern American accent.
One could still picture the Texan, but one could just as easily mistake the accent as being from anywhere in South America, such as Brazil.
Is there any way to more concisely say "an accent from the Southern States of the USA" without the ambiguity?