The stock was down 6.1 percent at $51.48 at midafternoon Monday in New York. Earlier, the shares slid as much as 11 percent to $48.55. Through last week, they had gained 20 percent in the past year.

The government Friday said it would fulfill a pledge it made as far back as 1998 to relinquish control of the Internet’s domain-name system. Gregg Moskowitz, an analyst at Cowen & Co., said the change in control and oversight increases the risk that VeriSign may not be able to renew its contracts in their current form to maintain the dot-com and dot-net registries.

“With the introduction of oversight uncertainty, and multiple stakeholders, we potentially could in a few years’ time see a less favorable outcome than present upon time of renewal,” Moskowitz wrote in a note Monday. He reduced his rating on the stock to the equivalent of hold from buy, while saying it’s unlikely that VeriSign will lose the dot-com contract when it comes up for renewal in 2018.

In a statement Monday, VeriSign said the National Telecommunications and Information Administration’s announcement doesn’t affect the company’s operation of the dot-com or dot-net registries, and that its agreements have presumptive rights of renewal.

“The announcement does not impact VeriSign’s dot-com or dot-net domain name business,” the Reston, Virginia-based company said in the statement. “The NTIA announcement involves Internet functions that are entirely different functions from those VeriSign performs under its dot-com and dot-net agreements.”