Manchester native Rashford, 19, and his United team-mate Jesse Lingard, 24, went to Manchester Children's Hospital on Monday and spent time with children hurt in the May 22 attack, which left 22 dead and 119 injured.
American pop star Ariana Grande, whose show was targeted in the suicide attack, put on a star-studded benefit concert in Manchester on Sunday and Rashford said it was vital for the city to pull together.
"We're with all the families as much as we can be and it's important that the families know that," he told reporters at England's St George's Park training base in Burton-on-Trent.
"That's one of the reasons why we wanted to go and visit the hospitals. We're doing as much as we can to support all the families and the victims of the attack.
"Things like the concert and going to the hospitals, it just shows the families and people around the city that everyone's together and we have to fight it together."
After a season that culminated in United's Europa League triumph against Ajax in Stockholm, Rashford has joined up with the England squad for Saturday's World Cup qualifier against Scotland and next week's friendly against France.
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With Wayne Rooney having again been overlooked by England manager Gareth Southgate, Rashford is the only United forward in the squad, but he does not believe Rooney's international career has run its course.
"Knowing Wayne, it's nowhere near over," Rashford said.
"The abilities he has and the things he can do on and off the pitch and the effect he has on all the players, he's still got a lot to do in his career and there's still a lot of trophies that England hope to be playing for."
An injury to Zlatan Ibrahimovic meant Rashford finished the season as United's main striker and he chipped in with crucial goals against Chelsea, Anderlecht and Celta Vigo.
Though Rashford does not turn 20 until October 31, he says the pace of his progress has come as no surprise to him.
"All that it's proved, to everybody else, is that the development is happening," he said.
"I already know it's happening. I know that I'm working hard in training every day and I can see the development in myself.
"For me to be playing the games and scoring some goals, it's just proof of my development."
He is not phased by the prospect of a white-hot atmosphere at Glasgow's Hampden Park either.
"It's just another experience," Rashford said.
"It possibly will be one of the toughest (atmospheres) I've faced so far and I'm hoping so, because it's another experience I can tick off the list and then I can keep moving forwards."