A potential strike against Verizon Communications Inc. has been avoided — at least for the moment.

Two unions representing Verizon workers have agreed to continue negotiations without implementing a strike. They said that enough progress had been made to justify continuation of talks.

Members of the Communications Workers of America and the International Brotherhood of Electrical Workers had earlier voted to strike if a new deal was not reached by last weekend. But on Saturday, CWA issued a statement saying “CWA, IBEW and Verizon are engaged in intensive negotiations in an effort to achieve a new collective bargaining agreement.” On Sunday, CWA said it agreed to “stop the clock” and postponed plans to strike.

“I believe they worked until 2 o’clock in the morning [Monday],” said Bob Mason, a CWA spokesman. “I haven’t heard anything since then.”

Mason said some union officials were hopeful that a deal could be reached sometime today.

“My experience with these things is it never goes as quickly as you hope,” Mason said.

The unions say the biggest remaining issues are job security and outsourcing.

The workers’ contract with Verizon expired Aug. 2.

More than 65,000 of Verizon’s workers are represented by Communications Workers of America and the International Brotherhood of Electrical Workers. Verizon has about 1,000 workers in the Albany, N.Y., area.

Union officials had said a strike by CWA and IBEW would be one of the largest in the United States in more than a decade.