Text messaging is an increasingly popular tool in American politics and an established one abroad. In his statement, Mr. Nelson acknowledged that the technology is “being harnessed by organizations and individuals communicating their diverse opinions about issues and topics.” He said Verizon has “great respect for this free flow of ideas.”

But the company did not retreat from its position that it is entitled to decide what messages to transmit.

Legal experts said Verizon’s position is probably correct under current law, although some called for regulations that would require wireless carriers of text messages to act like common carriers, making their services available to all speakers on all topics.

“This incident, more than ever, shows the need for an open, nondiscriminatory, neutral Internet and telecommunications system that Americans once enjoyed and took for granted,” said Gigi B. Sohn, the president of Public Knowledge, a consumer advocacy group.

Some of Verizon’s customers said they were outraged by the company’s initial stance.

Gary Mitchell, a lawyer in New Jersey, said he called a Verizon customer sales representative on this morning to cancel his wireless service in protest. After spending a few minutes on hold, he said, the representative read him an e-mail message that she said all the customer service representatives had just received. The message instructed representatives to tell callers that the policy had been reversed.

Verizon kept Mr. Mitchell’s business but lost some of his respect. “It was an incredibly foolish corporate decision,” he said.

Wyn Hoag, a photographer in California, said he was still considering whether to cancel his Verizon service.

“I’m a supporter of abortion rights, but I could be a Christian right person and still be in favor of free speech,” Mr. Hoag said. “If they think they can censor what’s on my phone, they’ve got another thing coming.”