The father-of-two was speaking at an event in Cardiff hosted by PinkNews.
The leader of Wales’ nationalist party has opened up about his own suicide attempt while walking home from a night out as a student in the 1990s.
In a moving speech, made during the PinkNews Cardiff summer reception, the father-of-two said: “I came here to Cardiff for university and even though we had a very active LGBT society there was something in me that was holding me back.
“I remember literally walking home from the centre of town with my eyes closed, hoping that I’d be knocked down by a car.
“It was my suicidal depression that many of us will identify with. Because I couldn’t find a way out for myself, I couldn’t see a road to happiness.
“I had no role models, I was basically taught to have a deep feeling of shame.”
Mr Price said he never imagined he would become a father and proud LGBT leader of a political party.
“One day, finally, I decided I’m going to love myself,” he added.
He called for the delivery of the government’s LGBT Action Plan, due to be published in the autumn, which he said he hoped would create “the kind of society that we want to see”.
Welsh Conservative leader Andrew RT Davies also took to the stage and admitted: “The Conservative Party don’t get everything right.”
Both leaders, and Labour ministers Jeremy Miles and Hannah Blythyn, committed to improving the rights of trans people in Wales.
Trans Aid Cymru co-founder Shash Appan told the politicians urgent action was needed to help and put in place protections for trans people, who she said are repeatedly vilified in the media.
Hitting out at the UK Government, Ms Appan said: “Transphobia is now Tory party policy.”
Among the party attendees was Jamie Wallis who became the first openly transgender MP after releasing a public statement in March.
He posted the statement online shortly after leaving a gathering for Tory MPs at which Prime Minister Boris Johnson reportedly made a joke about trans issues.
The event was the first in a series being hosted by global media company in each of the United Kingdom’s devolved administrations, with a final reception to be held within Westminster.
The purpose being to bring key politicians within each nation together with LGBTQ+-led businesses, charities and community members.
PinkNews founder and CEO Benjamin Cohen said he was impressed by what he saw as the cross-party “cohesion” between the Senedd members present, and their willingness to take on board the criticism levelled at them.
“You wouldn’t see this in Westminster,” Mr Cohen said.
“You won’t be finding the leader of the Tory party at the Westminster event.”