Desmond Swayne, who represents New Forest West, was asked to comment on the protests by one of his constituents.
In emails seen by Yahoo News UK, Swayne was asked to “show support to the black members of the New Forest community” by helping to instigate the “suspension of UK sales of teargas, riot shields and rubber bullets to the US”.
He was also asked to condemn “Trump’s use of force against his own citizens” after the US president pressed governors to put down violence sparked by Floyd's death.
Responding to the email, Swayne wrote: “Thanks. Sorry to disagree. Arsonists and looters have it coming.”
In another response to an email asking him to condemn Floyd’s death, Swayne responded: “Racism is a cancer, and I’m glad that the perpetrator is on a murder charge.
“Nevertheless, looters arsonists and rioters have it coming.”
Swayne’s comments were criticised by Labour MPs.
Jess Phillips said Swayne showed a “complete lack of thought or care”, while Florence Eshalomi tweeted: “Wow – what a response to a legitimate question from a constituent.
“I’m sorry your MP doesn’t seem to be able to show solidarity towards condemning racism and injustice with the local and national black community.”
Yahoo News UK has contacted Desmond Swayne’s office for a comment.
Former Minneapolis police officer Derek Chauvin has been charged with third-degree murder relating to Floyd’s death.
Protests quickly erupted in the US after footage of Floyd being arrested went viral.
Most protests passed peacefully on Tuesday night, and while there were scattered reports of looting in New York, the country appeared calmer than it did a day earlier, when violence swept through multiple cities.
One day after a crackdown on peaceful protesters near the White House, thousands of demonstrators massed a block away from the presidential mansion, facing law enforcement personnel standing behind a black chain-link fence.
The fence was put up overnight to block access to Lafayette Park, just across the street from the White House.
The crowd remained in place after the city's 7pm curfew passed, defying warnings that the response from law enforcement could be even more forceful.
But the protest lacked the tension of previous demonstrations. According to news agency AP, the crowd on Tuesday night was peaceful and polite.
At one point, the crowd booed when a protester climbed a light post and took down a street sign. A chant went up: "Peaceful protest!
Tuesday’s demonstrations followed Trump demanding that New York call up the National Guard to stop what he termed the "lowlifes and losers".
The president amplified his hard-line calls from Monday, when he threatened to send in the military to restore order if governors did not do it.
"NYC, CALL UP THE NATIONAL GUARD," he tweeted. "The lowlifes and losers are ripping you apart. Act fast!”
Protests have spread across the US, including in Los Angeles, Miami, Columbia, South Carolina and Houston, where the police chief talked to peaceful demonstrators, vowing reforms.
More than 20,000 National Guard members have been called up in 29 states to deal with violence.