European Union finance ministers piled pressure on Greece on Tuesday to remain in an international financial rescue program as the euro weakened on fears of disruption when Athens' credit lines expire in 10 days.

But as he returned to meetings on other, routine, matters with his EU counterparts in Brussels after the collapse of talks on Monday night, Greek Finance Minister Yanis Varoufakis dismissed their argument that his only option is to come back to them and ask to extend a bailout rejected by Greek voters.

"The next step is the responsible step," he said, offering no detail on what Athens was willing to propose. "We will continue to deliberate, in order to enhance the chances and actually achieve a very good outcome for the average European."