NASHVILLE (AP) - Local governments in Tennessee can no longer bar people with handgun carry permits from bringing firearms to parks, playgrounds and sports fields under legislation signed Friday by Republican Gov. Bill Haslam.

In a letter to the speakers of the House and Senate, Haslam said he remains concerned about potential unintended consequences for local leaders, but called the final version of the legislation a "vast improvement" from when it was first introduced.

"The final version of the bill made clear that guns are not allowed at school-related activities taking place in parks," Haslam said in the letter.

Critics of the measure disagree, arguing that the language is still vague because it bans guns "within the immediate vicinity" of school activities, but does not define a specific distance. The law carries no exemptions for playgrounds, greenways or ball fields where no school activities are taking place.

The content ious bill was drafted as a welcome gift from gun-friendly Tennessee lawmakers to the more than 70,000 people who attended the National Rifle Association's annual convention in Nashville earlier this month.

Democrats have been vocal critics, arguing it would endanger children playing Little League or climbing on jungle gyms.

During the legislative debate, freshman Sen. Jeff Yarbro persuaded colleagues in the upper chamber to add the state Capitol complex to the areas where handgun carry permit holders could be armed.

The Nashville Democrat said his amendment was aimed at highlighting what he called the "hypocrisy" of loosening gun restrictions near children, while keeping security in place around lawmakers.

The House voted to strip that amendment from the bill.

"The governor is right about the problems with this legislation, which takes power away from local governments and creates unnecessary confusion for schools, parents and gun owners alike," Yarbro said in an email. "I would have thought those problems would warrant a veto."

A law enacted in 2009 to allow guns in Tennessee parks included an opt-out provision for city and county governments. More than 70 communities initially decided to keep their gun bans in place - including in Knoxville, where then-mayor Haslam presided over a 2009 city council vote that kept in place a handgun ban in some of the city's parks.

Haslam in his letter said he's still concerned about local control.

"I know community leaders have the best sense of the specific activities taking place in their parks as well as the unique conditions that exist in and around those areas," he said. "Some of the most sensitive situations state and local leaders must consider are those activities involving school children."

It only takes a majority of both chambers to override a veto. That hasn't happened with any of Haslam's previous three vetoes. But lawmakers twice overturned vet oes by then-Gov. Phil Bredesen of legislation to allow permit holders to be armed in bars and restaurants that serve alcohol.

Republican Rep. Curry Todd of Collierville was the chief sponsor of the guns-in-bars legislation and led the veto overrides of 2009 and 2010, arguing that that the measure gave "law abiding citizens in this state a right to protect themselves."

Todd, who was also heavily involved in this year's guns-in-parks legislation, pleaded guilty to drunken driving and gun charges after a 2011 traffic stop in which he failing roadside sobriety test and police found a loaded .38-caliber gun stuffed next to the driver's seat.

Kathleen Chandler Wright, the head of the Tennessee chapter of Moms Demand Action for Gun Sense said she's disappointed with Haslam's decision.

"Moms across the state drew a line in the sandbox and urged legislators and Governor Haslam to reject this dangerous bill," she said. "And now parents will be left wondering whe ther the person standing next to their child on the swing set is carrying a concealed, loaded weapon."