Only 30 percent of long-distance trains were operating on Monday, with regional and urban services also limited by the walkout to 40 percent of normal levels, according to the national rail operator Deutsche Bahn.
The disruptions came despite last-minute efforts from the leadership of the rail company to bring the GDL drivers' union back to the negotiating table in the parties' pay dispute.
In a statement on Sunday, Deutsche Bahn offered to discuss a coronavirus-related bonus for drivers this year, something the union has previously demanded.
The suggestion was "a strong sign of willingness to reach an agreement" on behalf of Deutsche Bahn, the company's personnel director Martin Seiler said in a statement.
The drivers' union rejected the offer later on Sunday, describing it as a "smokescreen".
"With an offer not worth the paper it's written on, the trickster managers want to deceive passengers and in a targeted way spark anger and frustration against GDL," the head of the union Claus Weselsky said in a statement.
The strike action, announced last week, is the second in a wage dispute between GDL and German rail.
Earlier this month, the union led a walkout after its members voted 95 percent in favour of the move, following the collapse of talks with Deutsche Bahn.
The union is demanding a 1.4-percent pay hike plus a bonus this year, and a further wage rise of 1.8 percent in 2022.
Deutsche Bahn has proposed to phase in a 3.2-percent wage increase in two steps in 2022 and 2023.
The company's most recent offer did not put a figure on the bonus to be negotiated, while the GDL has demanded a premium of 600 euros ($703).
A walkout affecting Deutsche Bahn's freight services started Saturday at 2:00 am (0000 GMT). The strikes on both passenger and cargo services are due to end on August 25 at 2:00 am (0000 GMT).
