MCI Communications Corp. has turned a $500 million financing package into a $1 billion capital windfall that will allow the Washington telecommunications firm to speed up its massive construction program considerably.

MCI last week announced plans to raise $500 million by issuing a combination of 10-year notes and warrants that give investors the right to buy MCI stock at $55 a share.

Within hours after the offer was made, MCI's lead investment banker, Drexel Burnham Lambert Inc., told MCI executives the notes and warrants were so popular with investors that MCI easily could raise $1 billion if it wanted to. In the parlance of Wall Street, the original amount was "oversubscribed within hours."

It took MCI officials only 48 hours to decide that the company could digest the unexpected $500 million without upsetting its construction and financial plans.

They gave Drexel the go-ahead Friday, and by yesterday the entire $1 billion had been placed, said Drexel Burnham Managing Director Anthony Meyer. Investors have agreed to purchase the entire amount when the notes become available for sale next Monday.

Even for MCI, the company that decided years ago it could compete with American Telephone and Telegraph Corp., investor interest in its recent note offering was beyond belief.

The rapidly growing telecommunications business is a voracious user of capital, and MCI officials said they determined they would have no trouble spending the money.

MCI President V. Orville Wright said the company has a $1 billion capital spending plan in place for 1983 that will position MCI for the Jan. 1 breakup of the giant American Telephone & Telegraph empire.

Projects that will consume nearly all the funds MCI can earn, borrow or otherwise attract include:

* Installing 4,000 miles of fiber optic cable to transmit voice and data. MCI is ahead of schedule on the link between New York and Washington and will accelerate the work, a spokesman said.

* Adding more and bigger computer-switching equipment to give the company more flexibility in transmitting both voice and data.

* Expanding its international operations.

MCI recently won the Pittsburgh franchise to provide cellular mobile telephone service, and a spokesman said the company expects to win similar franchises in other cities.

Wright said that, although the offering sharply increases the company's debt, MCI executives feel that they can handle the larger debt load easily. The $1 billion note sale is by far the biggest fund-raiser in the company's history, easily surpassing the $400 million issue last year, Wright said.

As a result of the combined note-warrant sale, MCI's equity will rise from $823 million to $1.02 billion and its debt will climb from $962 million to $1.757 billion, Drexel Burnham's Meyer said.

MCI will realize $986.25 million from the offering, with the remaining $13.75 million going to Drexel and the other investment bankers. The investment bankers act as wholesalers, buying the entire offering from MCI, and then reselling the package of notes and warrants to investors.

The warrants permit investors to use either cash or the notes themselves to buy MCI stock at $55 a share any time in the next five years. There are 18 warrants attached to each $1,000 note, which pays 9 1/2 percent a year. On Aug. 22, however, MCI stock will split and MCI investors will receive a share of stock for each share they now own. The warrants will split, too. After Aug. 22, each warrant will permit the investor to buy MCI stock for $27.50 a share any time before Aug. 1, 1988.

MCI stock closed yesterday at about $39.37 on the over-the-counter market, down $2.50 a share.

Meyer said that the warrants are worth about $11 each in the current offering, and the notes are valued at 80 cents on the dollar.