UPDATE 1-AT&T, Verizon drop suits over network ads

* But Verizon will still use map comparisons in ads

* Both companies decline to comment

* Verizon shares rise 0.8 pct, AT&T shares up 0.6 pct

NEW YORK, Dec 2 (Reuters) - AT&T Inc (T.N) and Verizon Wireless have dropped legal cases against each other after a public battle over advertising their high-speed wireless services, but Verizon said it was continuing to advertise with maps that had started the fight.

AT&T had complained about ads from its bigger rival, a venture of Verizon Communications (VZ.N) and Vodafone Group Plc (VOD.L), and tried to stop it from using "misleading" coverage maps in a lawsuit filed in a court in Atlanta.

But on Wednesday it withdrew the case without saying why. Verizon Wireless also said that it dropped a case it had filed against AT&T in New York.

Both companies declined to comment on the legal cases, but Verizon Wireless said its "There's a Map for that" ad campaign was continuing with the same language and the same maps as before.

Shares in Verizon Communications were up 0.8 percent at $32.61 in early afternoon trading on the New York Stock Exchange, where AT&T stock was up 0.6 percent at $27.33. (Reporting by Sinead Carew; Editing by Tim Dobbyn) ((sinead.carew@thomsonreuters.com; + 1 646 2236186))