Amsterdam, Netherlands ? Garmin, the world’s largest maker of personal navigation devices, withdrew a $3.3 billion takeover bid for Dutch digital mapmaker Tele Atlas NV on Friday, clearing the way for rival TomTom.

Separately, Garmin said it struck a deal with Navteq Corp., the only other digital mapmaker other than Tele Atlas to have global operations, guaranteeing Garmin access to Navteq maps through 2015.

The navigation technology industry is undergoing rapid consolidation.

Garmin’s main rival, TomTom NV, made the first takeover bid for Tele Atlas in July. Garmin upped the price tag by 15 percent with an ensuing bid and countered with an offer of 2.9 billion euros ($4.2 billion).

In October, Finland’s Nokia Corp. announced last month it was buying Navteq for $8.1 billion (5.7 billion euros).

Friday’s news sent TomTom shares surging 7 percent to 60.70 euros ($89.02) in Amsterdam, while Tele Atlas shares dropped 8.7 percent to 29.30 euros ($42.97). Garmin shares jumped 16 percent, or $13.51, to $97.51.

Although Garmin, based in the Cayman Islands, with operational headquarters in Olathe, buys its maps primarily from Navteq, Garmin said it felt forced to challenge TomTom’s bid for Tele Atlas to ensure that both Navteq and Tele Atlas did not belong to competitors.

The logic is the same for all device makers: Owning one of the map makers will allow tighter integration of digital maps with the products that display them.

“When we made our original offer, we thought that Tele Atlas was undervalued based on TomTom’s original offer,” said Jessica Myers, a Garmin spokeswoman. “We were very willing to acquire Tele Atlas up to a certain price. But we felt there were diminishing returns for us beyond that level.”

Garmin and TomTom announced Thursday that they had reached an out-of-court settlement over patent disputes, leading many in the market to suspect a compromise on Tele Atlas was not far away.

Tele Atlas’ board has endorsed TomTom’s current bid of 30 euros ($43.95) per share. Den Bosch-based TomTom is Europe’s largest maker of automotive navigation devices, while Garmin is larger in the U.S. and overall.

Garmin Ltd. does use some Tele Atlas maps for regions in Asia, and Nokia and TomTom have all given assurances that they will continue to sell maps to all comers if they win their respective takeovers.