Verizon Communications Inc. reported a dozen cases of sabotaged cable lines and warned of delays in repairs and customer service on the second day of a strike involving about 45,000 employees.

The telecommunications company said there have been 12 acts of sabotage to telephone lines and to Internet and television services in Massachusetts, Maryland, New Jersey, and New York since the strike began.

Fiber-optic lines were intentionally cut in Tewksbury and several other municipalities on the East Coast, the company said.

Stolen equipment in Cedar Grove, N.J., affected service to a police department, and a heat system was tampered with at a central office in Manhattan.

“This could be a dangerous situation if people need to reach fire, police, or emergency responders and can’t use their phone,’’ said Phil Santoro, a spokesman for Verizon.

Verizon is offering a $50,000 reward “for information leading to the arrest and prosecution of individuals that intentionally damage Verizon cables or facilities or cause or attempt to cause physical injury to any Verizon employee or contractor.’’

Myles Calvey, a business manager with the International Brotherhood of Electrical Workers who is representing New England workers in the negotiations, said the union has no knowledge of its members committing any acts of sabotage.

“We don’t do that, and nobody in the union leadership supports any of that,’’ he said. The striking workers are members of the IBEW and the Communications Workers of America.

Verizon said the company met the demands of 75 percent of their customer repair orders on Sunday.

The company warned of longer hold times on their customer service lines and longer waits for repair service.

Verizon officials and leaders from the unions that represent the striking workers continued negotiations yesterday. About 6,000 workers in Massachusetts and about 800 in Rhode Island are on strike.

Workers continued to picket outside Verizon offices and stores in the region.

“We have to get these people back to work,’’ Calvey said. “Nobody wants all of these people out in the street.’’

Taryn Luna can be reached at tluna@globe.com.

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