He made the remarks on Friday ahead of this weekend's G7 Summit in Biarritz, France, his first international meeting as a Prime Minister, the BBC reported.
The Summit, a get together of most of the leaders of the world's largest economies, comes with just over two months until the UK is scheduled to leave the EU on October 31.
In his remarks, he insisted that the UK would be an "energetic partner" on the world stage after Brexit.
"Some people question the democratic decision this country has made, fearing that we will retreat from the world. Some think Britain's best days are behind us.
"To those people I say: you are gravely mistaken."
His comments come after French President Emmanuel Macron suggested a post-Brexit trade deal with the US could see Britain as a "junior partner" in a position of "historic vassalisation".
US President Donald Trump, who has consistently praised Johnson, has predicted a speedy US-UK trade deal after Brexit, the BBC reported.
But the British side is adamant that it wants to secure the right deal rather than a quick agreement.
A UK government spokesman said on Friday: "Of course we want to move quickly, but we want to get the right deal that works for both sides."
A Downing Street spokesman said Johnson and Trump "looked forward to speaking further" during their one-on-one talks on the sidelines of the summit on Sunday morning.
Also on Sunday, Johnson will meet European Council President Donald Tusk, who earlier this week refused the former's proposal to scrap the backstop plan for the Irish border.
( With inputs from IANS )