The three attackers were shot dead by police. Photo by Reuters/Clodagh Kilcoyne.
He told BBC Radio 4's Today programme: "We are actually increasing the number of armed officers, the numbers of police officers in our capital city has remained high".
Trump has used the policy, stalled now in USA courts, as an example of the sort of toughness that he says Khan refuses to show amid terrorism attacks that are riling the United Kingdom.
Khan tweeted that Trump's "ignorant" view on Islam "risks alienating mainstream Muslims".
On Monday morning, President Trump told a blatant lie while smearing London Mayor Sadiq Khan for the second straight day. "There's no reason to be alarmed", he had said. "We have constant attacks going on not just there but across the globe".
Before the origins of the London Bridge attack were even clear, Trump seized on it to promote his order restricting travel from Muslim-majority nations and lament that the Supreme Court is reviewing a "politically correct version". "There's no reason to be alarmed".More news: Britain's opposition leader calls on Theresa May to quit over police cuts
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Donald Trump has been blasted as "pathetic" and "truly beneath contempt" by Labour politicians for his latest attempts to smear Sadiq Khan.
The hostility between Trump and Khan began in the midst of the 2016 US presidential race, when, in May, Khan pummeled Trump for his statements about Muslims, calling Trump's view of Islam "ignorant".
This isn't the first time the Trump family has taken Khan's words out of context in an effort to smear him. "If we don't get smart it will only get worse".
The two men have history.
U.S. President Donald Trump on Monday doubled down on his criticism of London mayor's reaction after a couple of deadly attacks killed at least seven and injured dozens more.
Trump then takes Khan's remark out of context.
Trump and Khan have traded criticism since before the real estate mogul was elected U.S. president. "You've got to be prepared for these things, you've got to be vigilant".
In the article, Khan was reported as saying that being prepared for terror attacks was "part and parcel" of living in a major city.