The company, which is facing 42,700 U.S. plaintiffs, is widely expected to eventually buy itself out of the litigation, with analysts currently estimating the size of a future settlement at $8-$12 billion.
Bayer agreed with the plaintiff to delay for about six months a case in the California Superior Court for Lake County scheduled for Jan. 15, a company spokesman said in a written statement.
A second case due to begin on Jan. 21 in the California Superior Court for Alameda County would also be postponed until a date yet to be determined.
Bayer said the postponements would provide more time for it and representatives of the plaintiffs to "engage constructively in the mediation process".
The company, which acquired the weed killer brands last year as part of a $63 billion takeover of Monsanto, has ruled out pulling the products from the U.S. market, citing regulators and extensive research which have found glyphosate to be safe.
It will early next year appeal to reverse the first three U.S. court rulings that awarded tens of millions of dollars to each plaintiff.
Other trials initially scheduled for this year have already been postponed.
(Reporting by Ludwig Burger; Editing by Kirsten Donovan)