In a message marking Eid al-Adha, the prime minister called on people to celebrate the contribution made by the UK’s estimated 3.3 million Muslims.
“The story of Eid al-Adha is one of sacrifice, about doing your duty and doing what’s right,” Mr Johnson said in a statement.
“And that is something we see daily from Muslims right across the UK – men and women who, in all kinds of different ways, make such a huge contribution to modern British life.
“In business, in our public services, in culture and the media, at the highest levels of government and of course in England’s World Cup-winning cricket team, British Muslims are helping to make this country the success it is today.”
The prime minister praised the “extraordinary generosity” of Muslims, who traditionally celebrate by donating to charity and sharing meals with loved ones.
Prime ministers routinely release messages marking the two Eid festivals that take place each year, but Mr Johnson’s statement comes amid continued controversy over his previous remarks about Muslims.
He compared women who wear veils to “letterboxes” and “bank robbers” last year, but later apologised for the offence called.
The Muslim Council of Britain accused Mr Johnson of “pandering to the far right”, while his remarks were used by the perpetrators of hate crimes and included in a dossier calling for a formal investigation into Islamophobia in the Conservative Party.
YouGov polling released last month suggested 56 per cent of Tory members believe Islam was “generally a threat” to the British way of life, while two-thirds believed in the myth of no-go zones where “non-Muslims are not able to enter”.
Fiyaz Mughal OBE, director of the Faith Matters group, told The Independent the prime minister had been left with a “low standing” among British Muslims.
“Clearly he’s realised he can’t carry on like this,” Mr Mughal said. “He cannot govern a country with a large section of the population not feeling supported or part of the political process.
“This is a conciliatory tone he has taken and I think it’s part of a strategy of reconciliation and recognition of British Muslims.”
It came after the head of UK counterterror police called for politicians to “bring society together”.
Metropolitan Police assistant commissioner Neil Basu raised the alarm about increasing polarisation and said societal inclusion was needed to fight extremism.
Security services have been increasing efforts to combat far-right terrorism following a series of global attack and plots targeting Muslims, non-whites and perceived “traitors”.
Official UK threat level warnings now consider the extreme right-wing as well as Islamists, while MI5 has been brought into cases previously deemed “domestic” and left to police.
Of the terror suspects arrested in the year to March, 72 per cent identified themselves as British nationals or dual citizens, while 41 per cent were white, 36 per cent were Asian and 12 per cent black.
In his last major speech as home secretary last month, Sajid Javid appealed for a “national conversation about extremism” as he announced the government was drawing up a new strategy to combat multiple threats.
“We must act now, to avoid sliding into the barely masked racism of nationalism,” he said.
Eid al-Adha, also known as the “feast of sacrifice”, is celebrated by Muslims worldwide and honours the story of Abraham’s willingness to sacrifice his son at the command of God.
More than two million people have travelled to Saudi Arabia to undertake the Hajj pilgrimage to Mecca, which is the world’s largest annual gathering of Muslims and one of the five pillars of Islam.