AT&T announced that by the end of June it will have completed the rollout of its high-speed 3G network. In a statement issued today, the company said that it will deploy HSUPA technology in the six remaining markets across its entire wireless broadband network. The carrier also said that with the completed rollout of HSUPA, it will be the first U.S. carrier to fully deploy HSPA technology in its 3G network.

By the end of the year, AT&T says its 3G network will be available in nearly 350 markets, and that customers in those markets can expect uplink speeds between 500 kbps and 800 kbps and download speed of up to 1.4 Mbps with compatible devices.

“By fully deploying HSUPA across our 3G footprint, we not only meet the current needs of our customers but also lay the path for our continued evolution to even faster wireless broadband capabilities,” said Kris Rinne, senior vice president of Architecture and Planning for AT&T’s wireless operations, in a statement.

AT&T’s 3G announcement coincides with the rumors of a possible 3G iPhone launch in June.

AT&T also announced it will offer free Wi-Fi access to qualifying LaptopConnect customers at more than 17,000 hotspots. LaptopConnect customers will now automatically receive a pop-up message alerting them to Wi-Fi availability when in range of an AT&T hotspot. Customers with the latest AT&T Communication Manager software will only have to click Connect to switch to the available Wi-Fi network.

The offer is available to customers who subscribe to a DataConnect plan of $59.99 or more.