Environment Secretary Margaret Beckett spoke of her "deep regret" yesterday over the failure to meet the target for making single payments to farmers.
Ministers had promised that the bulk of the new payments, replacing previous subsidies, would be paid by the end of this month.
But the chief executive of the Rural Payments Agency, which is responsible for the scheme, was replaced earlier this month when it became known this would not happen.
Answering an emergency Commons question yesterday, Mrs Beckett said: "I fully understand and share the anxieties that these events will cause to the farming community and deeply regret that this unacceptable situation has arisen."
She said the RPA was now focusing on making the payments "as fast as is legally possible" under acting chief executive Mark Addison.
But shadow spokesman James Paice said Ministers were not absolved from the "catalogue of incompetence" and urged Farming and Food Minister Lord Bach to quit.
Mrs Beckett said she had been advised for the first time on March 14 that it would no longer be possible to make the bulk of the payments by March 31.
She said there were "substantial problems" facing the RPA in getting the payments to farmers - "much greater than had previously been reported to Ministers".
Speeding up the payments remained the "overwhelming priority" and steps were being taken to achieve this, she added.
Mr Paice said just six days ago a Defra newspaper landed on every farmer's doormat saying full payments were on track.
"I hope you are embarrassed at the very least, or ashamed, that this has happened."
He asked how many payments would now be made by the end of March and urged the Government to consider making interim payments.
"Theses delays are costing the industry £10 million to £12 million a month. Will the Government repay the interest on any related loan until the RPA issues the payment?"
Andrew Richards, senior food and farming adviser for NFU West Midlands, said if the RPA continued to make payments at the current rate, farmers would have to wait until the end of July for their money.
He said: "At the current rate all farmers won't get their payments until the end of July but no one is suggesting that is going to remain static. We have got to get the current payment rate above 1,000 farmers a week."