Boris Johnson must urge Donald Trump to "respect human rights" following protests over the death of George Floyd, the Labour leader has said.
In a letter to the prime minister, Sir Keir Starmer says the events "shone a spotlight on the racism" experienced by black and minority ethnic communities.
He also sought reassurance that UK exports were not being used in "the suppression of democratic rights".
Mr Johnson has said he was "appalled" by what happened to Mr Floyd.
Speaking at a press conference on Wednesday the prime minister said: "My message to President Trump, to everybody in the United States from the UK is that... racism, racist violence has no place in our society."
A video showing Mr Floyd, 46, being arrested on 25 May in Minneapolis and a white police officer continuing to kneel on his neck even after he pleaded that he could not breathe has triggered protests across the US and the world, including in the UK.
On Wednesday, thousands marched in London in a demonstration organised by the Black Lives Matter group.
Writing to Mr Johnson, Sir Keir said he was angered by Mr Floyd's death and "the response of US authorities to peaceful protest",
He said the UK has "a moral obligation to speak out" in defence of human rights and the "fundamental democratic right to protest".
He also asked the PM if his government had raised concerns with the US about the treatment of peaceful protesters; how the government would ensure UK exports are not being used "in the suppression of democratic rights" and what steps the government were taking to reassure black communities in the UK.
He said the death of George Floyd had "justifiably prompted anger and a burning desire for fundamental change".
"The UK must be clear in showing that we understand this frustration and that we are ready to stand together with those who seek to tackle the injustice and inequality that remains within all our societies."
'Lack of moral leadership'
During a radio interview First Minister of Scotland Nicola Sturgeon, when asked if President Trump was a racist, said: "I think sometimes it's hard to not conclude that, and what I always say when I'm asked questions that that is I can't see inside his head.
"But I do know that the language you use and how you express yourself matters and if you don't want to be accused of racism then don't use racist language, don't sound as if you are equating people who protest against racism with people who take to the streets in order to try to perpetrate racist values and attitudes."
She also suggested the US president was "displaying a lack of leadership, perhaps, a lack of moral leadership".
Meanwhile, Labour MP Dawn Butler has organised a cross party letter urging the government to halt the sale of tear gas, rubber bullets, and riot shields to the US.
Asked about the subject in the House of Commons, equalities minister Kemi Badenoch said: "Like all right-minded people, regardless of their race, I was profoundly disturbed by the brutal murder of George Floyd at the hands of the police.
"During these moments of heightened racial tension, we must not pander to anyone who seeks to inflame those tensions.
"Instead we must work together to improve the lives of people from BME communities."