The $100 (Â£80) Light Phone, a credit-card sized device which can only make and receive calls, received $415,000 (Â£334,000) from backers on Kickstarter.
Calls made to the owner's smartphone are forwarded to the phone, which has no internet functionality, via an app.
It was delayed by several months as the firm grappled with software issues.
"We've run into a few limitations in our initial user experience goals due to some iOS restrictions," Light Phone said in a statement.
"They are not going to affect the experience of being light, but will make turning on call forwarding a little bit more manual."
The Brooklyn-based company also apologised for missing its June shipping deadline and said the first batch of 1,800 white versions of the device will ship this month.
"We took on the ambitious task of building the software in-house with a small team in order to maintain ultimate control over the experience, however we regret not having methods for projecting accurate timelines," it added.
The phone has been manufactured by Foxconn in China.
Light Phone describes its product as a supplement phone, designed to help people "step away" from the distractions offered by smartphones when convenient.
"The phone is a very casual phone - if you're expecting an urgent call from your pregnant wife you shouldn't bring your Light Phone with you," founder Joe Hollier told the BBC.
It boasts 21 days of battery life and has no camera or contacts book, although users can programme 10 numbers to speed dial.
A black version of the phone will ship in January, the firm added.
The Light Phone contains a 2G micro Sim card for communicating with its "parent" smartphone but some backers are now expressing concerns on Kickstarter that the phone will not work in countries like Australia and Singapore where there are plans to switch off 2G.
Joe Hollier said the firm had contacted backers in affected regions and offered them refunds.
"Most people who launch a Kickstarter campaign set very ambitious targets about when they are going to ship," said analyst Ben Wood from CCS Insight.
"The grim reality is that it's not just about delivering the product, there are lots of things that go around it, like CE marking, regulatory approval and standards testing. It all takes time and costs money.
"A lot of consumer electronics projects find it takes a lot longer to get to market than they anticipated. For hardened Kickstarter enthusiasts this is regarded as the norm this days."
Mr Wood also said Light Phone was entering a competitive marketplace.
"It's an attractive design and a fun idea and will appeal to people who want to disconnect from the constant barrage of social media and everything else," he said.
"I think the challenge they have is there's a huge number of small talk/text phones available out there for very little money."

Passengers were terrified as a gust of wind sent empty carriages swinging at the top of the 60m (198ft) Sky Swing at Cardiff's Winter Wonderland.
Sayers Amusements, which operates it, said there was no fault with the ride.
It said it shut down automatically - as it should - when the wind got too strong on Friday.
The operator released a statement after it had investigated what happened on the towering ride.
It said when the ride started the wind had not exceeded the ride's  wind speed limit, which is 10m per second.
However, when gusts picked up the ride shut down.
"It took less than five minutes to get all gondolas unloaded," the operator said.
"No one was hurt as the safety system was working correctly at all times, and a full explanation was given to everyone on the ride, and they were all given a full refund, and all stayed onsite for a while afterwards."
It added that the ride re-opened after the wind eased.
The Winter Wonderland is a Cardiff Council event and the authority said it has sought assurances steps have been taken to ensure there is not another incident.
A crowdfunded handset designed to help people disconnect from their smartphones is due to ship at the end of November after a series of setbacks.
[NEXT_CONCEPT]
An amusement ride which was shut down after its carriages crashed into each other in mid-air with people on board is safe, its operator says.