Countries like France or the United States argue that while Germany is happy to rake in cash from selling its goods overseas, it fails to help other economies by spending at home to contribute to economic growth.
Merkel also defended her decision to hold this month's Group of 20 summit in Hamburg, Germany's second-largest city, where some demonstrations against the meeting devolved into violent street battles between police and protesters.
Asked in a television interview by ARD public broadcaster about her investment plans and Schulz's criticism, Merkel said: "We now can not spend the money that we have".
The German government's problem is rather bureaucratic barriers to allocating funds, which require accelerated planning processes, she said.
Schulz did not call for the lifting of the "debt brake" built into the German constitution by Merkel's conservative government in 2009, which sets legal limits on deficits in federal and regional budgets.
Domestically, Schulz urged the state to spend more on faster internet connections, roads and rail, renewable energy and education.
Vel d'Hiv: les images de l'arrivée de Benjamin Netanyahu et Emmanuel Macron
Ils ont été retenus quatre jours au Vélodrome d'hiver, à Paris, puis emmenés dans des camps puis déportés. Moins d'une centaine de ces raflés - et aucun enfant - survécurent.
"If you want to be a state leader in Europe, you must acquire the trust of the peoples", Schulz said. "We say, for example, that we have to use at least one third of the additional tax revenues for investment". Schulz, a former president of the European Parliament has a formidable opponent in Merkel.
He argued for the creation of greater German financial contributions to the bloc's budget, to which it contributes 15 billion euros ($17.2 billion) after paybacks into Germany are calculated.
He also supported the idea of an European Union finance minister.
After running practically neck and neck with the CDU, the SPD has stumbled to nearly 20 percent behind Merkel's conservatives. The party, which is the junior coalition partner with the CDU, has often struggled to find major policy platforms and issues that separate it from Merkel, who is viewed by many as a steady and reliable hand after 12 years in office.
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