Investigators were questioning 17 suspects held in Britain in connection with the botched July 21 bomb attacks on London's transit system; authorities released three other suspects detained in raids.
The government said it was trying to extradite from Rome one of the suspected attackers; Italy also arrested two brothers of that suspect.
British police are investigating possible links between the terror cell that killed 52 people when it bombed three Underground trains and a red double-decker bus on July 7, and a second cell that targeted the same transportation system two weeks later but caused no deaths when their bombs failed to fully explode.
Police say the four suicide bombers who carried out the July 7 attacks are all dead. And they believe they have arrested all the failed July 21 bombers.
On Tuesday, Underground officials restored full service on the Hammersmith and City line and the District line, which were partially shut down after the July 7 bombing at Edgware Road station.
Two other lines remain closed or suspended. Officials say they hope to reopen the closed stretches of the bombed Piccadilly line later this week but do not know when full service will resume on the targeted Circle line.
British Transport Police continued its highly visible policing operation across the capital's subway system and overland rail network on Tuesday, spokesman Simon Lubin said. Officers in bright yellow jackets were posted outside many stations, although the police presence was not as strong as on Thursday, when a massive force patrolled the network exactly three weeks after the first attacks and one week after the second attempt.
Home Office minister Hazel Blears also planned the first in a series of meetings with representatives of Britain's Muslim community amid increasing complaints that young Muslims were being targeted by police in stop-and-search operations.
"Just picking people up on the basis that they are Muslim is never going to get the results that we want," Blears told the British Broadcasting Corporation's Radio 4 on Tuesday, reversing her earlier support for the controversial police initiative.
"Tackling terrorism is absolutely dependent on the confidence of these communities to feel that they can come forward, give information and be part of the fight against this threat."
Meanwhile, Britain is also "pursuing extradition" of Hamdi Issac, one of the four suspected July 21 attackers who is being held by police in Rome, Blears said.
Issac was charged Monday in Italy with association with the aim of international terrorism and possessing false documents, his lawyer Antonietta Sonnessa said. She raised the possibility that investigations in Italy against Issac could hold up his extradition. "One cannot possibly define the timing of the extradition process," she told The Associated Press on Tuesday.
But Italian police said he would soon be extradited to Britain, and Blears told British Broadcasting Corp. radio that "it's my understanding that there are no domestic charges" against Issac that might delay his extradition.
Carlo De Stefano, head of Italy's anti-terror police, said the investigation so far indicated that Issac was "part of a loosely knit group rather than a well-structured group."
De Stefano did not say whether he thought Issac's cell had ties to the earlier bombers. Italian media have reported that Issac said the group was not linked to either the July 7 attackers or the al-Qaida network.
Sonnessa told Britain's ITV News the plot was put together the day before, "in a meeting with this group of friends."