Hispanic people were targeted in an apparent hate crime when a gunman in El Paso shot dead 22 people last Saturday.
Trump himself has been accused of stoking hatred against Hispanic people.
He came to Texas from Dayton, Ohio, where he had visited a hospital to meet survivors of a shooting in which nine people died, the BBC reported on Wednesday.
Trump said before leaving Washington that he was concerned about "the rise of any group of hate... whether it's white supremacy" or any "other kind of supremacy".
But the Democratic congresswoman who represents El Paso, Veronica Escobar, is refusing to meet him, saying his "racist and hateful words and actions" had caused pain to her community and her country.
The El Paso shooting is being treated as a possible hate crime.
Much of the city identifies as Hispanic and the suspect is thought to be the author of a text posted online which said "this attack is a response to the Hispanic invasion of Texas".
The text echoed some of the US president's language, with Trump having frequently used the term "invasion" to describe the situation on the US-Mexico border.
Police have still to establish a conclusive motive for the Dayton attack but say they have uncovered evidence "that the shooter was exploring violent ideologies".
Attempts by Trump and others to link the shootings to mental illness have been criticised by healthcare professionals.
On Wednesday, the president said he did not "want guns in the hands of sick people" and was "looking to do background checks".
( With inputs from IANS )