Southgate raised his concerns last week that female fans and members of the LGBTQ+ community may not travel to support England due to rights restrictions in Qatar.
The safety and conditions of migrant workers used to build the stadiums to host the tournament have also been a source of concern.
"I feel like as a group, we've never shied away from important issues and we've always had our opinions," Kane told reporters on Wednesday.
"We've always tried to show unity in anything that we've done. So that's what will happen now over this camp and the next camps."
Kane has had discussions with Tottenham team-mate and France skipper Hugo Lloris over the potential for captains to come together and make a joint gesture of solidarity at the World Cup.
"It's important to understand that first of all, as players we didn't choose where this World Cup was going to be," Kane said ahead of England's friendlies against Switzerland and the Ivory Coast.
"But what it has done is shone a light on important issues that might not have come to light if the World Cup wasn't there.”
"As always, we try and help in any way we can. We try and use our platform to help in any way we can. I understand there's been some progress on certain issues in the country so far,” he added.
"So my hope is that having the World Cup there and having this light on the country will help try and progress some of the issues that have obviously been going on for a long time."