The Irish prime minister has pledged to open an investigation into the €30bn (£25.5bn) bailout of Anglo Irish Bank as it emerged that an executive sang "Deutschland, Deutschland, über alles" as colleagues joked about German money flowing into the country after a state guarantee of the institution's deposits.

A banker is heard on tape joking and singing the former first lines of the Deutschlandlied – not used since the Nazis made the first stanza their anthem – as the bank's then chief executive, David Drumm, urges his executives to "get the fucking money in". The recording was made in September 2008, when the Irish state stepped in to rescue a bank brought low by a property lending spree.

Enda Kenny, the taoiseach, paved the way for a parliamentary inquiry into an "axis of collusion", although he stopped short of a full, Leveson-style inquiry. Referring to the former taoiseach Brian Cowen, who ran the country during the Anglo Irish bailout, he said: "I assume that our predecessors here, people who served … in high office and in those governments, would have the opportunity and would have the willingness, I assume, to come to a parliamentary inquiry."

The latest recordings to be leaked from inside the bank will compound national outrage in Ireland over the behaviour of Anglo Irish bankers.

Dublin intervened in September 2008 with a guarantee of the bank's deposits to keep it afloat – a move that angered London and Berlin because it enticed money from British and German savers.

Cowen's blanket bank guarantee, much criticised as foolish by other European Union governments, was designed to prevent Anglo's immediate collapse but instead put Ireland on a slippery slope to bailing out all six Irish-owned retail banks. In one conversation, two days after the fateful bank guarantee, Drumm giggles while his colleague John Bowe, then director of capital markets, recites lines from the Deutschlandlied.

Drumm, who has since fled to the US, and Bowe are heard laughing about fears that the guarantee would drive a wedge between Ireland and its EU partners.

The former said he would give "two fingers" to UK concerns.

Bowe was recorded boasting that he had picked as the cost of the state rescuing them a random figure, of €7bn (£5.9bn), "out of my arse".

Ireland's deputy prime minister, Eamon Gilmore, admitted on Tuesday ministers had been unaware the recorded conversations existed, even though the state has owned the bank since it was nationalised in 2009.

He said the degree of arrogance and hubris of the bankers highlighted in the tapes was shocking, and made clear the need for a full parliamentary inquiry into the Irish banking collapse.

"That's why we have brought forward legislation to establish such an inquiry, and I hope that the legislation will be enacted before the summer and we can get on with it," Gilmore told RTÉ radio. Gilmore added that the revelations couldcompromise Irish attempts to win further debt relief from the European Union. "It makes it more difficult, of course it does, but we're going to continue to work to get the best possible outcome for the Irish taxpayer," he said.

Kenny later confirmedthat the country's that police had had the Anglo Irish Bank tapes for four years. He told the Dáil they had been originally handed over to the Gardai when they began their when criminal investigations into the bank.

His cabinet colleague, the finance minister, Michael Noonan, confirmed that he, too, was unaware of the tapes, even though it was standard procedure to record calls between senior banking personnel.

Recordings obtained by the Irish Independent of Drumm joking about the rescue plan on the tapes will intensify anger in Ireland towards the top bankers, given that he remains in exile in Boston, allegedly owing the state €8m.

Bowe has denied trying to mislead the state, adding that the reported remarks were "off-the-cuff comments".".

The secret tapes have compounded suspicions that Anglo Irish Bank's senior executives had lured the then Fianna Fáil-led il-led government into a costly financial trap in the autumn of 2008. The figure of €7bn cited by Bowe more than quadrupled, to €30bn.

During the Irish boom, Anglo Irish Bank became the preferred lender to property speculators and builders. Among its high-profile clients was Ireland's one-time richest man Seán Quinn, who borrowed hundreds of millions of euros from the bank to fund a global property portfolio stretching from the US to the Ukraine and Russia. When the world property market crashed, Quinn's empire crumbled, leading him to bankruptcy and prison.