The 19-day nationwide telephone strike will continue indefinitely, the Communications Workers of America announced yesterday, because some of the union's 34 regional units failed to reach agreement with local telephone companies, which CWA accused of a last-minute effort to erode past contract gains.

"CWA's strike against the Bell System will continue in all parts of the country until we have signed such local agreements," said Glenn E. Watts, president of the 525,000-member union.

"The phone company has misread us twice," Watts said, "They didn't believe we would strike, and they didn't believe we would resume our strike" if all 34 regional agreements were not concluded by the deadline of 12:01 a.m. Thursday.

American Telephone & Telegraph Co., most of whose 675,000 unionized workers remained off the job, said that nine of its subsidiaries--including Chesapeake & Potomac Telephone Co.-- failed to reach agreement despite all-night bargaining Wednesday night and early Thursday.

By late last night, C&P reportedly was one of four local bargaining units still without tentative agreements. The local talks, which were recessed early in the evening, are to be resumed this morning.

Union officials, however, would not say which contracts, or how many, were unsettled, but said "several remain reasonably far apart."

Two other unions, the International Brotherhood of Electrical Workers and the Telecommunications International Union, which together represent 150,000 phone workers, have tentatively settled contracts but have not returned to work at many locations where CWA continued picketing.

Officials of both AT&T and CWA, who approved a three-year nationwide contract last Sunday, had been optimistic that the strike would be settled by yesterday. "I didn't think local issues would prolong the strike," Watts said, "But in place after place, the companies introduced issues that were not there before."

Noting AT&T's record $7.2 billion profit last year, Watts said local subsidiaries were looking to "fatten their next quarter profits and shareholder returns" by taking hard lines in local bargaining.

C&P is saving $13 million per week in wages during the strike, according to estimates by CWA, which said it would ask public utility commissions to consider the savings when deciding rate increase requests.

AT&T officials disputed the union's characterization that the phone companies were determined to seek "retrogressions" in contracts but company spokesmen would not discuss bargaining. AT&T said local bargaining strategies were strictly the prerogative of local company executives.

Wages, health benefits and some job security provisions have already been negotiated in the national agreement, which remains in effect.

But various job security issues have remained local stumbling blocks, officials said, particularly because of the impending Jan. 1 breakup of AT&T into seven regional firms. The current contract will be the last nationwide telephone agreement, and many phone company employes are deeply concerned about possible loss of jobs.

A key local problem is that C&P is attempting to downgrade or "de-skill" various jobs and eventually eliminate them, said George R. Strick, vice president of CWA District 2, which represents 34,000 C&P workers in Maryland, Virginia, West Virginia and the District of Columbia.

As technology advances, Strick said, C&P wants to assign more high-skill tasks to lower-paid employes, with the aim of phasing out the higher pay categories and cutting jobs. "What the hell good is a wage increase, if your job is not there?" he said.

C&P spokesman R. Webster Chamberlin said the contract talks were stalled primarily on the question of "the amount of flexibility which the company would have in assigning, dispatching and utilizing the work force."

"We want to bargain," Chamberlin said, "We want the strike resolved and we want our people back to work."

CWA stepped up picketing yesterday at dozens of C&P work sites in metropolitan Washington. But as the strike neared the end of its third week, a small number of union members were reported to have crossed the picket line and returned to their jobs.

"I'll stay on strike as long as I have to" to assure job security, said Barbara Lee, 31, a $281-a-week phone company clerk who picketed yesterday in Northwest Washington. Lee said she talked to several CWA members who crossed the line "and they said they just had to work to pay their bills." Those crossing the picket face fines by the union, officials said.

Both AT&T and C&P said basic telephone service has not been significantly disrupted by the strike, but they reported weeks-long backlogs for new installation or rearranging of phone systems and for nonemergency repairs.