An anarchist organisation has claimed responsibility for two attacks on railway signalling in Bristol which caused severe delays and the cancellation of services.

British transport police and Network Rail have confirmed that signalling cable was destroyed on Tuesday morning in two separate incidents of arson which caused "extensive damage" and substantial delays to passengers.

The group – calling itself the Informal Anarchist Federation – has warned of further "guerrilla" attacks and sabotage to "hurt the national image and paralyse the economy however we can". On Wednesday the group posted a statement on the Indymedia Bristol website saying it had "struck two points on the railway routes into Bristol", adding that members had "lifted concrete slabs running alongside the tracks and burned out the signalling cables found in the trench underneath".

The group said the points on the track had been chosen to target employees of the Ministry of Defence, "military industry companies" such as Raytheon, Thales, HP and QinetiQ, and the "corporate hub of Bristol". It promised further attacks, saying: "Finance, judicial, communications, military and transport infrastructure will continue to be targets of the new generation of urban, low-intensity warfare."

It described Tuesday's actions as guerrilla activity and said it had "no inhibition" about using such methods again. Characterising the Olympics as a "spectacle of wealth" in a time of austerity, it ended the statement saying it wanted "civil war" and that anarchy was "unavoidable".

Network Rail said that in the first attack, discovered at 4:15am by a passing train driver near Parson Street station in south Bristol, cabling was dug up and wrapped in material which was then set alight.

The second attack was spotted at 11:37am near Patchway railway station in the far north of the city.

The train operator First Great Western said normal services had not fully resumed until the following morning.

Transport police say that the two incidents "may or may not be connected". They are appealing for further information.

Network Rail and First Great Western described this type of deliberate attack on railway lines as "very rare"; most vandals target trains or infrastructure that they can sell for scrap.

Detective Chief Inspector John Pyke said: "We are aware of a statement posted on the internet in which a group is claiming responsibility for these incidents. At the moment, this is one of a number of lines of inquiry officers are investigating. This was completely irresponsible behaviour and we will do everything possible to trace those responsible and bring them to justice."

Anyone with any information is asked to call British transport police on 0800 40 50 40, or the independent charity Crimestoppers on 0800 555 111.