Larry Barton, professor of public safety at the University of Central Florida and a threat assessment instructor for the Federal Bureau of Investigation, said the strategy saves lives, but people need to make decisions quickly.
Britain was already on high alert following the attack on a concert by USA pop star Ariana Grande in Manchester, northwest England, in which seven children were among the dead.
On Saturday, three attackers drove a hired van into pedestrians on London Bridge then ran into the bustling Borough Market area where they stabbed numerous people.
Theresa May stated that the two attacks were not connected when it comes to planning and execution, although she did state that they were the result of the same "evil ideology of Islamist extremism", which she calls a perversion of Islam and the truth.
May responded to the attack by calling for an overhaul of the strategy used to combat extremism, including a demand for greater global regulation of the internet, saying big internet companies were partly responsible for providing extreme ideology the space to develop. After it had stopped, three men got out of the vehicle and ran into a nearby area with bars and restaurants and frantically started stabbing people.
Twenty-one of the 48 people injured are listed in critical condition, reports The Guardian.
A vigil will be held on Monday evening near London Bridge in honour of the victims of the attack, which took place at around 10pm, while a minute's silence will take place at 11am on Tuesday.
London Metropolitan Police said raids were continuing in Barking.
In their first joint appearance overseas, Mr Mattis and Mr Tillerson spoke alongside their Australian counterparts at the opening of a joint meeting expected to touch on a range of subjects including defeating the Islamic State group, stabilising Afghanistan and dealing with North Korea's nuclear threats.
Islamic State, losing territory in Syria and Iraq to an advance backed by a US-led coalition, had sent out a call on instant messaging service telegram early on Saturday urging its followers to carry out attacks with trucks, knives and guns against "Crusaders" during the Muslim holy month of Ramadan. Neighbors at the site of one major raid in Barking said a man who lived there resembled one of the attackers shown in news photographs. We will review the counter-terrorism apparatus.
One of the attackers shouted "this is for Allah" as he knifed a man near a pub.
May, who served as Britain's interior minister from 2010 to 2016, said there was too much tolerance of extremism in Britain.
In response, Mr Trump tweeted: "We must stop being politically correct and get down to the business of security for our people".
"The Conservative party will not be campaigning nationally today".
"My baby brother lost the love of his life on the London Bridge", Cassie Ferguson Rowe wrote on Facebook. "I was just throwing it at them, trying to get them to chase me so I could get them out into the main road where the police could see them and obviously take them down".
"We were in an Uber (taxi) going towards London Bridge and suddenly we saw people running".