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Build-up to the tournament has been marred by some fans booing players taking the knee in solidarity with the fight against racism.
England begin their tilt at the Euros title against Croatia on Sunday and Southgate wants the nation to come together, bolstered by his players’ performances on the pitch.
"I think it's time for the country to unite, full stop," Southgate said.
"If the team can be a catalyst for that then that's brilliant. I think the England team is often a catalyst for bringing people together ... so of course in the process of doing that we want to play well, we want to win, we want to excite people, but not all of that falls upon us."
Southgate says it was time for England to "remember what a strong nation we are", adding: "We've had lots of division and sometimes we need to remember what a strong island we are, what a strong nation we are, the great qualities that we have.
"There were moments at the beginning of the pandemic that were so powerful where people did pull together, I think we should always be striving towards that.