Army bomb disposal experts and police began searching a flat at Westgate End, close to the city centre, on Sunday afternoon, after a 41-year-old man was arrested on suspicion of drug offences in Leeds earlier that day.
Counter terrorist officers are still investigating after police found "potentially suspicious material" at the address.
A spokeswoman from The North Easter Counter Terrorist Unit (CTU) said this morning: "A 41-year-old man has been further arrested for offences under the explosives act. He is still in custody."
Police cordoned off an area of Westgate whilst they carried out investigations on Sunday night. People were also evacuated from nearby properties.
Road closures were lifted yesterday morning but a safety cordon remains in place as the CTU, supported by West Yorkshire Police, continues its enquiries.
In a statement issued yesterday, the CTU said: "Whilst the search continues, public safety remains the priority of investigating officers.
"At this time, this is being treated as an isolated incident.
"Residents will be kept as informed as possible and we are grateful for their understanding, patience and support while the search is concluded."