Dutch Finance Minister Dijsselbloem, who heads the Eurogroup of the 17 eurozone nations, said finance ministers had reviewed positively the situation in Spain, whose overextended banks had to be bailed out in June 2012.
Spain was rescued to the tune of €100 billion, and has used €41.3 billion of these funds to date.
But the country's "economic and budgetary outlook has improved," Dijsselbloem said, with Madrid set to complete its rescue programme by year-end.
Whether Spain would need "accompanying measures" to get them through the transition would be discussed in November, he added.
"The general idea is that the bank (rescue) programme will be shut down at the end of the year," he said at a press conference at the end of meeting.
"No single country has said (that Spain) has to accept more money or another programme with conditions," he added.
"The good news is that the Spanish programme is right on track and I hope that they can leave the programme successfully at the end of the year," said Jörg Asmussen, the German representative at the European Central Bank, also on Monday.
This will be music to the ears of the Spanish Government led by Prime Minister Mariano Rajoy.
After Monday's meeting of finance ministers, Dijsselbloem also said eurozone ministers also discussed the Single Supervisory Mechanism, a key step towards the bloc's planned banking union.
"The SSM is expected to come into force in coming weeks," Dijsselbloem said, apparently after Britain's concerns over how it would work were satisfied.
Non-euro Britain is home to the European Banking Authority, which is supposed to draft the rules for all banks in the bloc, while the SSM is to be run by the ECB.
To ensure that the 17 eurozone members did not out-vote the 11 non-euro members also grouped in the EBA, London won agreement in December that there would have to be a 'double majority' in both camps for any action.
A UK diplomatic source said London had won fresh assurances that this would be the case and accordingly, EU finance ministers could clear the SSM when they meet here Tuesday.
Asmussen said progress on the SSM was "really very good news... We can (now) really speed up preparations... (for) a banking union."
French Finance Minister Pierre Moscovici said the banking union was the main issue and "a priority for France."
"We want a global banking union, complete and ambitious," he said, confirming that the SSM would be finally cleared on Tuesday.
The SSM is to be complemented by a Single Resolution Mechanism to close failing banks and a Deposit Guarantee regime protect savers.
This is meant to provide a comprehensive, single regulatory framework to prevent taxpayers having to fund the disastrously expensive bailouts which led to years of austerity and recession the eurozone is only now emerging from.
EU finance ministers were warned Monday of the "dramatic consequences" a US debt default could have as they discussed how to prevent failing banks from ever again collapsing their own economies.
With US President Barack Obama holding yet another round of talks to head off a first US debt default on Thursday, EU Economic Affairs Commissioner Olli Rehn said it was vital a solution was found.
"Otherwise it could have potentially dramatic consequences on the world economy and on the still nascent recovery in Europe," Rehn said.