Tim Marshant of Longmeadow said cancelling travel plans would be giving the terrorists what they want.
Islamic State has claimed responsibility for the attack. Other key questions are whether the know-how to build the device was obtained from a plethora of DIY guides on the internet, or from another person.
The terror threat level was previously raised to critical in May after Manchester.
The blast went off at 8:20 a.m. local time and sent commuters scrambling in a panic.
Pictures and video posted on social media show a white plastic bucket inside a foil-lined shopping bag, which appeared to have wires coming from it, on the floor of the subway vehicle. The BBC understands the device had a timer.
Professor Hans Michels, an explosives expert from Imperial College London, said the device appeared to have largely failed.
An image made from a video showing burning items in an underground train at the scene of an explosion in London Friday, Sept. 15. However, none of the victims are said to be serious.
The president of the Board of Deputies of British Jews, Jonathan Arkush, put out a statement shortly after the attack.
British prime minister Theresa May will chair a meeting of the national security committee at 1.00 pm (1200 GMT).
British Prime Minister Theresa May rebuked U.S. President Donald Trump over his tweets about the London train terror attack on Friday and said the bomb was created to cause "significant damage".
Mr Rowley asked the public to remain "vigilant", but said they should "not be alarmed".
Trains were suspended along a stretch of the Underground's District Line, and several homes were evacuated as police set up a 50-meter (150-foot) cordon around the scene while they secured the device and launched a search for those who planted it.
The President used his third tweet about the attack to push his so-called Muslim travel ban in the USA, saying it should be "far larger, tougher and more specific".
A police officer told MailOnline: 'We believe there is a second bomb, people need to stay back there is a man with knives on the loose'.
Passenger Peter Crowley was sitting in the carriage, travelling from Wimbledon, when the explosion happened.
"We heard the first scream and we saw a flash and smoke and people started running immediately", he told NBC News. "I looked up and saw the whole carriage engulfed in flames making its way towards me", Ola Fayankinnu, who was on the train, told Reuters.
Witnesses described seeing at least one passenger with facial injuries.
"The explosion occurred at the Parsons Green station in Fullham, which is about four miles southwest of Big Ben".
In the three years until March this year, police foiled 13 potential attacks but in the next 17 weeks, there were the four attacks while the authorities thwarted six others, Rowley said.