A strike on German passenger rail began early Monday, creating headaches for thousands of travellers and commuters, after the train drivers' union rejected a new offer to keep services going.

In a statement on Sunday, rail operator Deutsche Bahn offered to negotiate a coronavirus-related bonus for drivers this year.

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.

-With a coronavirus bonus we have met one of the union's key demands. There is no longer any reason to refuse to return to the negotiating table- Seiler said.

The GDL 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 walk-out 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 made no mention of the value of the bonus to be negotiated, while the GDL has demanded a premium of 600 euros ($703).

As the strike began, only one in four long-distance passenger services were operating.

A walk-out 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).