The Real IRA has admitted bombing two banks in Northern Ireland as well as the UK City of Culture office in Derry, and has warned that it will continue to target economic interests.

In a statement to the Guardian laced with anti-capitalist rhetoric, the Real IRA said the bombings and future targeting of the banking system were its response to bankers' "greed" and were meant "to send out the message that while the Irish national and class struggles are distinct, they are not separate".

The attacks and the language used in attempting to justify them appeared designed to tap into the widespread public loathing of the banks on both sides of the Irish border.

The republican dissident group was unapologetic about bombing the office of the UK City of Culture 2013 in Derry last week. It said the office was a symbolic target because the City of Culture award to Derry underpinned British rule.

In its most bellicose warning yet to the banks on both sides of the Irish Sea and the border, the Real IRA said: "The IRA has recently carried out a number of bomb attacks on the banking establishment.

"Such attacks are an integral part of our strategy of targeting the financial infrastructure that supports the British government's capitalist colonial system in Ireland. The impetus to carry out this type of attack is directly linked to pressure from working-class communities in Ireland as a whole.

"At a grassroots level, working-class communities are suffering most from the effects of cuts to essential services and poverty is now endemic. Families who have lost income as a result of the financial crisis – caused by the bankers – are being intimidated and some are being evicted from their homes."

The organisation added that "the ruling class of bankers and politicians are disconnected from the consequences of their disastrous policies and decisions".

In May, masked men threw a holdall containing a device into Santander's branch in Derry city centre. In August, a bomb was thrown into Santander in Hill Street, Newry. A Real IRA bomb caused major damage to a branch of the Ulster Bank in Derry last year.

The terror group attempted to link the banks to the Police Service of Northern Ireland. "In the six counties, the effective power of the system is vested in heavily armed PSNI units who, ultimately, enforce bank repossessions of homes, vehicles, etc," it said. "The PSNI is not a police force, it is a political militia and a social control tool designed to protect the interests of the British establishment whether financial or political."

In September last year, the Real IRA had issued a warning that banks and bankers could be targeted.

As well as the attack in Derry's Guildhall Square last week, a bomb was left there on 12 October last year. The organisation predicted such incidents in the runup to Derry becoming a City of Culture in 15 months' time.

The Real IRA statement said: "The IRA has also carried out bombing operations against the so-called UK City of Culture offices in Derry city centre. It should be obvious that our objection is focused on the political exploitation of Derry's name and culture. Republicans view this charade as an elaboration of the well-choreographed 'peace process' which resulted in former IRA personnel serving as British ministers.

"This time, the whole nationalist community is expected to join in celebrations of their place within the United Kingdom and thereby realise the Thatcherite policy of regarding the six counties as being 'as British as Finchley'. Expressions of Irish identity within the context of 2013 will be effectively 'licensed' by the organisers under the banner UK City of Culture."

The group added: "The timing of the UK City of Culture is linked to the economic crisis: cash-strapped businesses naturally follow the carrot of increased revenue in 2013, politicians under pressure to produce jobs are totally compliant, anyone who objects is smeared or labelled a 'dissident'. The goodwill of our communities is being held to ransom, critical thinking is seen as dangerous, whole communities are being encouraged to adopt a herd mentality. The IRA will continue to challenge this; resistance will continue."

The bombing of the City of Culture office caused outrage throughout Derry and beyond, with hundreds demonstrating against the attack.

A Real IRA representative also told the Guardian that the Sinn Féin deputy first minister, Martin McGuinness, was under no physical threat. McGuinness, a candidate for the Irish presidency, has claimed his life has been under threat from republican dissidents in recent years. "Why would we turn him into a so-called martyr?" the Real IRA representative said.