Angry protesters have told US President Donald Trump there is “blood on your hands” as he visited the cities grieving from last weekend’s mass shootings.

Mr Trump met victims and first responders from last weekend’s deadly shootings in Texas and Ohio as chanting protesters accused him of inflaming tensions with anti-immigrant and racially charged rhetoric.

He and his wife, Melania, visited hospitals where victims were treated in El Paso, Texas, on the border with Mexico, and in Dayton, Ohio, after massacres 13 hours apart that shocked the US and reopened a national debate on gun safety.

In both cities, crowds of protesters gathered to confront Trump and condemn his visit. Some held signs reading “Trump is racist”, “Love over hate” and “Send him back”.

In Dayton, chanting crowds urged Mr Trump: “Do something!”

He and Mrs Trump avoided the media on both hospital visits and stayed out of public view.

They visited survivors in their hospital rooms at the University Medical Centre in El Paso and Miami Valley Hospital in Dayton, and thanked the medical staff and first responders, White House spokeswoman Stephanie Grisham said.

“It was a warm and wonderful visit,” Mr Trump said on Twitter after leaving Dayton. “Tremendous enthusiasm & even Love.”

Mr Trump also visited law enforcement personnel in El Paso to thank them for their response on Saturday, when a man killed 22 people at a Walmart store, apparently after posting an anti-immigrant statement online.

In Dayton, nine people and the suspect were killed in a rampage early on Sunday.

“The job you have done is incredible,” Mr Trump told gathered officers. “I wanted to come and thank you.”

Angry protesters lined the President’s route through Dayton. Photo: Getty

Mr Trump said he wanted to strengthen background checks for gun purchases and make sure mentally ill people did not carry guns. He predicted congressional support for those measures but not for Democratic efforts to ban assault rifles.

“I can tell you that there is no political appetite for that at this moment,” the President said at the White House.

“There is a great appetite, and I mean a very strong appetite, for background checks.”

Dayton Mayor Nan Whaley and US Senator Sherrod Brown of Ohio, both Democrats, accompanied Mr Trump in Dayton and urged him to call on Senate Republican leader Mitch McConnell to bring the Senate back from recess to work on a House-passed bill that expands background checks on gun buyers.

El Paso residents await Donald Trump’s visit on Thursday. Photo: Getty

Mayor Whaley said she agreed with Mr Trump’s decision not to visit the district where the shooting occurred, given the high emotions in the community.

“A lot of people that own businesses in that district are not interested in the President being there,” she said. “A lot of the time his talk can be very divisive and that’s the last thing we need in Dayton.”

Mr Trump later criticised the two Democrats for their comments, saying on Twitter that their news conference was “a fraud. It bore no resemblance to what took place”.

Protesters in Dayton also heckled Ohio’s Republican governor Mike DeWine at a vigil for the shooting victims, with chants of “do something”.

Donald and Melania Trump arrive in El Paso. Photo: Getty

Americans remain on edge following the twin attacks. On Wednesday, a backfiring motorcycle in New York’s Times Square, which sounded like a gun shot, sent frantic people scrambling for cover while in Virginia, the headquarters of the USA Today newspaper was evacuated over reports of a man with a weapon in the building.

New York Governor Andrew Cuomo said “people are obviously very frightened”.

“You hear a noise, you run. That’s the state of this nation. We’re petrified,” he said.

The New York Police Department tweeted a reassurance after it received multiple 911 calls about the tumult on Tuesday night.

“There is no ActiveShooter in TimesSquare. Motorcycles backfiring while passing through sounded like gun shots,” the department said.

“Please don’t panic. The Times Square area is very safe!”

On Monday, Mr Trump gave a speech focusing on mental health reforms, tighter internet regulation and wider use of the death penalty.

Democrats accuse the President of hiding behind talk of mental illness and the influence of social media, rather than committing to laws they insist are needed to restrict gun ownership and the types of weapons that are legal.

The words of a president matter. They can move markets. They can send our brave men and women to war. They can bring peace.

And they can unleash the deepest, darkest forces in this nation — like Donald Trump has chosen to do.

— Joe Biden (@JoeBiden) August 7, 2019

Democratic presidential front-runner Joe Biden planned say in a campaign speech in Iowa that the US has a president with “a toxic tongue” who has embraced a political strategy of hate, racism, and division.

While Mr Trump was on his way to Texas, Mr Biden accused him of fanning “the flames of white supremacy”.

-with AAP