The Australian bank confirmed that it had made an offer for Abbey, but said merger talks had now ended.
"The discussions regarding the National's proposals did not result in any agreement and have now ceased," NAB said in a statement.
News of NAB's withdrawal came one day after Abbey rejected a rival takeover approach from Bank of Ireland, saying it was not in shareholders' best interests. The Australian bank's retreat clears the way for Bank of Ireland, which is expected to pursue its bid for Abbey.
Abbey National rejected the approach from the Bank of Ireland, saying it would prefer to push ahead with its existing restructuring plans. A merger between the two companies would create Europe's 11th biggest bank, with a market value of about £15 billion ($21 billion). In a statement to the London Stock Exchange, Abbey National said its board had unanimously concluded that the proposal was not in the best interests of its shareholders.
Bank of Ireland said it was surprised Abbey National had "adopted such a position without any engagement or discussion between the two companies". In a statement the bank said it had given Abbey sufficient detail of its intent, of the financial benefits for shareholders and of the structure of a combined group to merit discussions.
Even if Abbey National fends off Bank of Ireland, it is considered to be a takeover target. It has issued several warnings about profits and currently has no chief executive.