The arrest of Gen Augusto Pinochet (82) has shocked and split Chile, with rightwingers condemning his detention and leftists applauding it.
The senator's arrest in London "was a cowardly act", Mr Luis Cortes Villa, executive director of the Augusto Pinochet Foundation, told local media.
The foundation gives educational scholarships to military families.
"A very good piece of news that breaks the circle of immunity," Ms Viviana Diaz of the protest group Families of the Detained and Disappeared was quoted by Santiago newspapers as saying.
Chile's Communist Party held a mass street party in central Santiago yesterday to celebrate the arrest.
News of his arrest made banner headlines on front pages of national newspapers. Their editors have in the past been blocked by their owners from making headline news out of Gen Pinochet because of the still-considerable power he wields.
Mr Ricardo Lagos, a centre-leftist leading in the polls to be the next president after elections in December 1999, said Chile should not become embroiled in a judicial matters on foreign soil because it would damage the country's image.
Local media said Gen Ricardo Izurieta, the general who took over as commander-in-chief of the army from Gen Pinochet only in March, met late on Saturday with the Interior Minister, Mr Raul Troncoso. On hearing of the arrest, Gen Izurieta apparently interrupted a holiday in the south of Chile and cancelled a scheduled trip to Chilean bases in the Antarctic to return to the capital.
Chile's government on Saturday condemned his arrest, saying it violated Gen Pinochet's diplomatic immunity granted to him as a senator. The British Foreign Office said he has no diplomatic status in Britain and it was entirely a judicial matter.
Chile's army said the arrest was "unjust and undesired" and urged President Eduardo Frei's government to move to end it.
In the capital, Santiago, a group of about 200 pro-Pinochet demonstrators gathered on Saturday outside the British embassy to protest over the arrest. There was a scuffle when an anti-Pinochet activist spoke up in defence of the detention.
In the US, the Washington Post quoted President Salvador Allende's widow, Ms Hortensia Bussi de Allende, as saying: "I am experiencing profound happiness that what couldn't happen in Chile is finally happening abroad."