With over a day since Verizon Wireless' LTE network went down, Verizon says it is now getting closer to restoring the service.

We have determined cause of 4G LTE issue & are working with major vendors to restore connections. Details as they come, the company announced on Twitter last night.

In a statement Verizon spokesman Jeffrey Nelson confirmed that there was a problem, noting that 4G smartphones like the Thunderbolt were still able to make calls. There is no word on what  caused the outages.

On Thursday morning some Verizon subscribers have reported that their service has returned. Verizon says it plans to restore service on a market-by-market basis.

In an update on Twitter, the company said it is investigating the issue, acknowledging that Thunderbolts making voice calls may get 1XRTT data, meaning that the phone gets a voice connection only. Thunderbolt phones can work on the 3G network, but that doesn't offer the speed of data transmission that LTE does.

So far, the only phones that support Verizon's 4G LTE network is the HTC Thunderbolt and Samsung's Droid Charge, which was originally supposed to go on sale today. But Verizon pushed back the release date, citing unexpected delays. No new rollout  date has been given.

The outage comes just after Verizon Vice President Nicola Palmer said that she expected more issues from the company's 4G LTE since its December rollout. The surprise here to me is the speed bumps were very few and far between and they didn't do any damage to the undercarriage, she said on Monday.