Counter-terror detectives also found a device they described as "not viable" at an address in southwest England and security was stepped up on the Tube network in a bid to reassure the public.
The first item, found on Thursday on a train at North Greenwich station, which serves the O2 entertainment complex in southeast London, was still being examined yesterday.
A controlled explosion was carried out on the item.
The 19-year-old was arrested by armed police in London on Friday. An electric stun gun was used during the arrest on a busy shopping street, but no shots were fired.
Yesterday, a court in London gave police permission to hold the man until 12:20 pm (1120 GMT) on Friday.
Detectives have been "working tirelessly since the item was found to follow up all potential leads", police said in a statement.
"Officers are keeping an open mind regarding any possible motive. They are not looking for anyone else in relation to this investigation at this stage.
"The public will see more officers, including armed police, in and around transport hubs to provide reassurance around public safety."
Those officers evacuated the address and erected a 200-metre cordon around it but the item was later declared "not viable".
Britain's current national terror threat level has been set at severe -- the second highest of five -- since August 2014, meaning an attack is considered highly likely.
The Times newspaper spoke of a "lone wolf" and said that the incident was "feared to be the first credible bombing attempt on the London transport network in more than 10 years".
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