The Home Secretary said police have made "good progress" with their investigation.
The "severe" threat level now in place means officials believe another attack is highly likely.
But on Sunday, Ms Rudd announced it was being downgraded.
Britain remains on its highest level of alert on Sunday, meaning another attack is believed to be imminent.
Following the bombing of a London tube train at Parsons Green station on Friday, the terror threat level was increased from severe to critical.
She said his claim that Scotland Yard had the bomber "in their sights" was not based on an intelligence leak and was "pure speculation".
Responding to reported Isis claims that its followers have manufactured further explosive devices in London, Ms Rudd said: "They will always make claims that suit their intentions, but actually there is no evidence of that".
She added that the Joint Terrorism Analysis Centre (JTAC), which sets the terror threat level, had decided "sufficient progress has been made" to lower it.
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Following the arrest police searched an address in Stanwell, Surrey, where a forensics team and several police vehicles were seen in attendance.
Police are continuing to search a foster home in Sunbury-on-Thames, Surrey, in connection with the teenager's arrest on Saturday.
Of the 30 people injured in the bombing, all but one have been discharged from hospital.
The 21-year-old man was arrested in Hounslow shortly before midnight last night.
Two men, aged 18 and 21, have been arrested in connection to Friday's bombing.
The entire road was evacuated on Saturday while the initial investigations at the property were underway.
Friend Alison Griffiths said the couple had an 18-year-old and a 22-year-old staying with them recently.
The two arrests indicate authorities believe the attack at the Parsons Green station was part of a coordinated plot, not the act of a single person.