Boris Johnson has told his fellow Brexiteers they should not “gloat” about the UK’s departure from the EU, which he said was a cause for “hope not fear”.
The foreign secretary urged people to “unite about what we all believe in”, an “outward-looking, confident” UK.
Leaving the EU was not a “great V-sign from the cliffs of Dover”, he said.
Mr Johnson also said the result cannot be reversed and that Britain should not be bound by EU rules after Brexit.
And he questioned the economic benefits of being in the EU single market and customs union, which the government plans to leave.
Mr Johnson was one of the leading figures in the 2016 Leave campaign, and has previously been accused of undermining Prime Minister Theresa May’s Brexit strategy.
But he was on his “best behaviour” and “stuck rigidly to the script” with this speech in central London, BBC assistant political editor Norman Smith said.
Pro-EU campaigners hit back at his overtures to Remain voters – with Labour MP Chuka Umunna describing the speech as an “exercise in hypocrisy”.
And Conservative MP Sarah Wollaston accused him of an “optimism bias” about the benefits of Brexit.
In seeking to build bridges with the other side of the EU debate, Mr Johnson said he risked “simply causing further irritation” and accepted he would not “persuade everybody” but added: “I have to try. In the end these are people’s feelings and people’s feelings matter.”
Leaving the EU would allow the UK to play a greater role on the world stage, rather than becoming isolated, he said.
“We must accept that many [Remainers] are actuated by entirely noble sentiments, a real sense of solidarity with our European neighbours and a desire for the UK to succeed,” he said.
“If we are to carry this project through to national success – as we must – then we must also reach out to those who still have anxieties.
“I want to try to anatomise at least some of those fears and to show to the best of my ability that they are unfounded and that the very opposite is usually true: that Brexit is not grounds for fear but hope.”
According to Mr Johnson, Brexit is “not some great V-sign from the cliffs of Dover”, but was “the expression of legitimate and natural desire to self govern of the people”.
“That is surely not some reactionary Farageist concept,” he added in a reference to the former UKIP leader.
Alongside his calls to Brexit supporters not to “gloat” and “sit back in silent satisfaction”, Mr Johnson said holding another referendum on the UK’s membership of the EU – as some campaigners are calling for – would be a “disastrous mistake that would lead to permanent and ineradicable feelings of betrayal”.
“Let’s not go there,” he said.
He also said the UK must regain control of its regulations and tariffs – and that continuing to be bound by EU directives would be “intolerable” and “undemocratic”.
Mr Johnson said the benefits of being in the single market and customs union were “nothing like as conspicuous or irrefutable” as claimed by their supporters, claiming other countries were able to trade with the EU without paying membership fees.
And arguing for independence on setting regulations for businesses, he said British people should not have laws affecting them “imposed from abroad” when they have no power to elect or remove the people making them.
However, during a transition period immediately after the UK leaves in March 2019 things would “remain as they are”, he said.
Mr Umunna, of the Open Britain campaign, said Mr Johnson had talked of taking back control – but that the government had withheld information about the impact of Brexit from Parliament.
“We are already a great country, we are already internationalist and we are already global,” he said.
Mr Johnson’s speech was the first in a series of speeches by Theresa May and her ministers on the “road to Brexit”.
The prime minister is expected to address the UK’s future relations with the EU in a speech in Munich on Saturday, the day after she holds talks with German Chancellor Angela Merkel in Berlin.
Ministers are under pressure to spell out how they can square their desire for frictionless trade after Brexit with the UK’s exit from the single market and customs union, which EU officials say will create trade barriers.
By leaving the customs union, the UK has said it will have freedom to negotiate trade deals of its own during the transition period, while reducing tariffs on imports from developing countries.
Meanwhile, a report by the Commons Home Affairs Committee has said the UK is ill-equipped to cope with changes to the immigration system after Brexit due to a lack of resources.
The government has yet to set out in detail what type of immigration model it wants to set up outside the EU, when it will no longer be bound by freedom of movement rules from Brussels.
The MPs warned this posed an “immense bureaucratic challenge” and that “rushed and under-resourced changes will put border security at risk”.