"It's about the question of one currency. This common European currency ... must remain stable."
Angela Merkel, Germany's chancellor, also sought to reassure the euro zone that her country was behind a joint EU-International Monetary Fund (IMF) package.
"What we need is a quick reaction for the stability of the euro zone as a whole and everything that takes us away from this central goal is at the moment not an option ... we do not need uncertainty, but certainty," she said.
The German government, which is the largest single contributor to the bailout package with a $11.2bn loan, is reluctant to vote on the deal until after May 9 elections in the country's most populous state - North Rhine-Westphalia.
Schaeuble's promise of making the May 19 deadline would see aid arrive as Athens has to refinance an $11.3bn euro bond.
"I reported Greece's needs to the parliamentary leaders and requested that we arrange the parliamentary debate and decision process so that we are in a position - like the others - to make the necessary loans available to Greece before May 19, if needed," he said.
He said that any failure by Athens to refinance the euro bond on May 19 would have unforeseeable consequences.
Germany may be able to finalise a law granting Greece financial aid on May 7, but the opposition Social Democrats said they would not back an accelerated parliamentary process to approve aid.
Jens Bastian, an economist at the Hellenic Foundation for European and Foreign Policy, said that Germany's government was stalling on the issue for "political domestic consumption".
"I am asking myself why are we still waiting, what is delaying the activation of this programme," he said.
"We have lost in many ways already three to four months. We could have had it earlier at a much less cost, and in particular much less agonising for Greece and its citizens."
Saddled with huge debt and a swollen deficit, Greece bowed to pressure from markets on Friday and formally requested aid, triggering what could be the first financial rescue of a member of the 11-year-old currency bloc.
Athens is in talks with the EU and IMF on additional steps to get the aid flowing in time to meet the May 19 debt deadline.
Greece has already announced billions of euros in budget cuts, including tax hikes and reductions in public sector wages, setting off violent protests and strikes.
Meanwhile dockers at Greece's largest ports stopped work on Monday to protest against moves to allow non-Greek cruise ships to moor at multiple Greek ports without hiring Greek crews.