BERLIN, July 18 (Reuters) - The economic upswing in Europe is gaining momentum and Germany is ready to deepen euro zone integration as long as risks and liabilities arising from political decisions remain linked, German Finance Minister Wolfgang Schaeuble has told lawmakers.

"Despite or even because of Brexit, European integration remains one of the best ideas that Europeans had in the 20th century," Schaeuble said in a letter, seen by Reuters on Tuesday and sent to lawmakers from Chancellor Angela Merkel's conservatives and the co-governing Social Democrats (SPD).

Germany and France now had to work closely together and pull in the same direction to strengthen cooperation in the soon-to-be 27-member bloc, the veteran politician said, urging all euro zone governments to further implement structural reforms, reduce debt and make their budgets more sustainable.

"Germany advocates a steady implementation of these (fiscal) agreements and is also ready to more effectively prevent future crises and further deepen the monetary union," he said.

"The rule for this is simple and convincing: To set the right incentives and avoid non-sustainable developments, risks and liabilities must be at the same level and in one hand."

French President Emmanuel Macron has said Europe must complete an imperfect single currency through the creation of a joint euro zone finance minister who would oversee a pooled budget for investments and transfers intended to help member states cushion downturns. (Reporting by Michael Nienaber; Editing by Madeline Chambers)