United Airlines officials said yesterday that construction of the airline's new $15 million passenger terminal at Washington Dulles International Airport is on schedule and said that United will begin service May 1 with 58 departures a day to 18 cities along the East Coast.

The opening of the United terminal, along with the opening of American Airline's hub operations in Nashville on April 15, mark the beginning of intensified competition for travelers flying north and south along the Atlantic seaboard. American also plans a hub at the Raleigh-Durham, N.C., airport, which is expected to open in a year.

"Both American and United, as the two biggest carriers, have been primarily east-west carriers," said Robert J. Joedicke, an airline industry analyst with Shearson/Lehman Brothers Inc. "As they expand to become national carriers, the next step is to get into the north-south routes, particularly in the heavy traffic area east of the Mississippi."

The opening of the hub at Dulles is part of the new pattern of competition in the airline industry in which companies compete with hubs (operations centers from which an airline connects to a large number of destinations). The idea is to keep passengers on a single airline as long as possible.

With the hub at Dulles, United is also taking on Eastern and Delta, which have long-established hubs in Atlanta; Piedmont, with hubs in Charlotte, N.C., and at Baltimore-Washington International Airport; USAir, with a hub at Pittsburgh, and People Express, Presidential and New York Air.

United Senior Vice President William Speicher, general manager of United's eastern division, said the airline plans to price its fares to meet the competition.

Speicher said the fares will include a one-way, off-peak coach fare to Boston of $49 and a regular fare of $79. First-class service off-peak will be $89, compared with a regular first-class fare to Boston of $119.

A one-way coach ticket to Miami during off-peak hours will be $119. During peak travel hours, the fare will be $139. First class to Miami will be $149 off peak, and $169 regularly, he said.

United has flown out of Dulles for many years on east-west routes to Chicago, Denver, Los Angeles and San Francisco, but its new hub operation adds service to Cleveland, Boston, Hartford, Conn., Rochester and Buffalo, N.Y., New York City (LaGuardia), Newark, Norfolk, Raleigh-Durham and Wilmington, N.C., Columbia and Charleston, S.C., Savannah, Ga., New Orleans, La., and in Florida to Tampa, Orlando, Fort Lauderdale and Miami. United provides service now between those cities and other destinations.

United's service to Chicago will continue to operate from the main Dulles terminal, but its other flights will operate out of the new, mid-field terminal that the airline is building. Mobile lounges will ferry passengers between the two terminals continuously, Speicher said.

Carrington Williams, chairman of the Washington Dulles Task Force, said that the Federal Aviation Administration is working on plans to end the problem of traffic jams at the exit gates of the airport's parking lots. "It's not a shortage of parking. It's a shortage of exits, and that's being remedied," he said.