Media playback is not supported on this devicePremier League players kneel in Black Lives Matter solidarity
The Premier League says its Black Lives Matter campaign is to send the message that it is unacceptable to treat black people differently to anyone else - and not an endorsement of a political movement.
A series of tweets from the Black Lives Matter UK account about Palestine has prompted criticism.
The Premier League said in a statement it was "aware of the risk posed by groups that seek to hijack popular causes to promote their own political views".
"These actions are entirely unwelcome and are rejected," it added.
After the tweets were posted on Sunday, Labour leader Sir Keir Starmer told BBC Breakfast it was a "shame" the sentiment behind the Black Lives Matter movement was "getting tangled up with these organisational issues" and said it was "nonsense" for the group to call to "defund the police".
The Black Lives Matter movement has led to global protests against racism and police brutality following the death in the United States of George Floyd, an unarmed black man, while a police officer knelt on his neck.
The Premier League has shown its solidarity, with players' names replaced on the back of their shirts with 'Black Lives Matter' for the first 12 matches of the restarted season, and a Black Lives Matter badge will feature on all shirts for the rest of the campaign.
But while 'Black Lives Matter' has become the slogan behind the protests, Black Lives Matter also exists as a global organisation, founded in 2013, with several goals including to advocate against white supremacy and police violence towards black people.
In its statement, the Premier League said it stood alongside players, club and a wide range of football organisations who had "come together in recent weeks to reject racism and to show support for the message that black lives matter".
The league said "Black Lives Matter" had become an "expression of unity for people from all communities who believe it is unacceptable to treat black people differently to anyone else".
"In an unprecedented move, Premier League players from all 20 clubs united in solidarity with this message and the Premier League supported their request to replace their names on the back of playing shirts with 'Black Lives Matter'," the statement added.
"The Premier League offered this backing as we wholly agree with the players' single objective of eradicating racial prejudice wherever it exists. And we are unequivocal in the belief that there is no room for racism in our competition, football as a whole, or the wider community."
Explaining that "professional football bodies and the players and managers recognise the importance of the message that black lives matter", the league added: "We do not endorse any political organisation or movement, nor support any group that calls for violence or condones illegal activity.
"We are aware of the risk posed by groups that seek to hijack popular causes and campaigns to promote their own political views.
"These actions are entirely unwelcome and are rejected by the Premier League and all other professional football bodies, and they underline the importance of our sport coming together to declare a very clear position against prejudice. We want our message to be a positive one that recognises football has the power to bring people together."