The terror threat level in the United Kingdom has been reduced from "critical" to "severe" in the wake of the Parsons Green terror attack.
Thirty people were injured when an improvised explosive device caused a fireball on a District Line carriage.
In a statement, Ms Rudd said: "Following the attack in Parsons Green last Friday the police have made good progress with what is an ongoing operation".
Home Secretary Amber Rudd said police were "working hard" to track down those responsible for the blast.
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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"Severe" means a terrorist attack is thought to be highly likely, whereas "critical" suggests it is imminent.
So far police have arrested two men, aged 18 and 21, and are searching properties in Sunbury-on-Thames and Stanwell in west London. He is being questioned at a south London police station but has not been charged or identified.
Police arrested an 18-year-old man in the departure lounge of Dover port earlier on Saturday in what they called a "significant" step and then raided a property in Sunbury, a town near London and about 6km from Hounslow.
The entire neighborhood around their house was evacuated as a precaution when the search began Saturday.
Of the 30 people injured in the bombing, all but one have been discharged from hospital.