MADRID (Reuters) - Spain's borrowing costs shot up at a bond auction on Thursday, after economic data confirmed the country is back in recession and reports of an outflow of deposits from nationalized Bankia hammered its share price. Spanish Prime Minister Mariano Rajoy said on Wednesday his government, struggling to reduce its budget deficit, could soon find it difficult to fund itself affordably on the bond market unless the pressure eases. His finance minister, Cristobal Montoro, meets heads of finance of all 17 regions later to review their budget plans which are a crucial plank of the drive to lower public debt. The European Commission warned last week that stubbornly high debts in the regions and the welfare system would prevent Spain meeting its deficit goal of 5.3 percent of GDP this year. El Mundo newspaper reported that customers at troubled Bankia SA had taken out more than 1 billion euros ($1.3 billion), equivalent to around 1 percent of the lender's retail and corporate deposits, over the past week. The government denied there had been an exit of funds, but the bank's shares dropped more than 20 percent at one stage, extending the previous session's loss after it delayed publishing fourth-quarter results. "It's not true that there is an exit of deposits at this moment from Bankia," said Economy Secretary Fernando Jimenez Latorre. The government last week took over Bankia, the country's fourth-largest lender which holds around 10 percent of Spanish deposits, in an attempt to dispel concerns over its ability to deal with losses related to the 2008 property crash. Spain's deposit guarantee fund guarantees 100,000 euros per customer. I have two accounts with Bankia and up to now I have not closed them. I'm not even considering it," said Jose Ignacio Gonzalez, 42. It must be more secure with the backing of the state, it has a guarantee. The government told the sector last week to set aside another 30 billion euros in provisions, prompting some analysts to say much more would need to be done. A government spokeswoman said the bidding to select an external auditor to value real estate assets across the banking sector was still open, denying Oliver Wyman and BlackRock had been chosen as sources previously told Reuters. While Greece, facing fresh elections which could hasten its exit from the euro zone, has dominated headlines, uncertainty over the final cost of Spain's banking reform has raised the prospect that it could require an expensive international bailout, a bill the euro zone would be stretched to cover. Official data confirmed the Spanish economy shrank by 0.3 percent in the first quarter, putting it back into recession and facing a prolonged downturn as the government cuts spending in an attempt to wrestle down its budget deficit. Unemployment is already running close to 25 percent, rising to around 50 percent among the young. The government will publicize budget plans from 17 powerful autonomous regions later on Thursday, possibly rejecting some of them if they do not make deep enough spending cuts and giving local officials 10 to 15 days to redo them. If the regional budgets are not approved by the end of the month, the central government can invoke a new law and take control of spending. The regions must cut 15 billion euros out of their budgets, after their overspending last year caused Spain to miss its deficit reduction target badly.