The attacks in Dayton and El Paso left 31 people dead.
President Trump spoke out on racism and hatred following the shootings but has been accused of stoking the same sentiments he sought to condemn.
The Democratic congresswoman who represents El Paso said she would not meet him, urging him to understand that his words “have consequences”.
“I refuse to join without a dialogue about the pain his racist and hateful words & actions have caused our community and country,” Veronica Escobar tweeted.
The El Paso shooting is being treated as a possible hate crime. Much of the city identifies as Hispanic or Latino 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 Mr Trump having frequently used the term “invasion” to describe the situation on the US-Mexico border.
What sort of welcome will Trump get?
Ms Escobar is not the only one to suggest Mr Trump faces a cool reception in El Paso. Beto O’Rourke, a native of the city and Democratic presidential challenger, said Mr Trump “has no place here”.
Both he and Ms Escobar have said they will attend a community event intended to honour those who died and “confront President Trump and white supremacy”.
El Paso’s Republican Mayor Dee Margo said it was his “formal duty” to welcome Mr Trump but added he would “continue to challenge and harmful and inaccurate statements made about El Paso”.
Mr Trump this year inaccurately described El Paso as one of the most dangerous cities in the US as he sought to advance his border wall scheme.
He could also face protests on his first stop in Dayton. Mayor Nan Whaley, a Democrat, urged people to “stand up” and said she planned on telling “how unhelpful he’s been” on addressing gun violence.
How has he responded to the shootings?
In a speech on Monday, he said: “In one voice, our nation must condemn racism, bigotry and white supremacy.
“These sinister ideologies must be defeated,” he added. “Hate has no place in America.”
He called for mental health gun control reforms, the death penalty for those who commit mass murder and more bi-partisan co-operation over gun laws.
But the address drew criticism for not saying enough on gun control.
The White House has defended Mr Trump’s visit and accused Democrats of politicising a moment of national tragedy.
White House spokesman Hogan Gidley said it was “ridiculous” to blame Trump for the El Paso shooting “You have to blame the people here who pulled the trigger.”
What happened in the two attacks?
In El Paso on Saturday a gunman opened fire in a crowded Walmart, killing 22 people and injuring 24 more.
A suspect, named by US media as Patrick Crusius, was arrested at the scene shortly after.
The 21-year old has been charged with capital murder, meaning he could face the death penalty.
Just hours later in Dayton, Ohio, shooting began in an area popular for its nightlife
Police killed the gunman, 24-year-old Connor Betts, within 30 seconds of him opening fire but that was long enough for him to kill nine people.
Among the dead was Betts’ sister, Megan. CCTV footage obtained by CNN showed the two drinking together at a nearby bar a couple of hours before the shooting began.