The United States reached an agreement yesterday with Taiwan, its largest supplier of textiles and clothing, that sharply restricts the growth of that country's textile shipments over the next two years, chief textile negotiator Charles R. Carlisle announced.

The agreement comes as the Reagan administration is trying to get its three top textile suppliers -- Taiwan, Hong Kong and South Korea -- to agree to limit the growth of their shipments to the United States in the face of heavy congressional pressure for even sharper cutbacks and a July 31 deadline for renegotiating a new multi-fiber arrangement (MFA) that covers world textile trade.

The United States reached an agreement with Hong Kong two weeks ago that is similar in the scope of its restrictions to the Taiwanese pact. South Korea remains the lone holdout among the big three textile suppliers, and U.S. trade officials said they were unsure whether they could reach a satisfactory agreement with that country.

Carlisle called the Taiwan agreement "a second, vitally important step in the administration's efforts to prevent surges in textile imports."

But the U.S. textile industry denounced the agreement with Taiwan, as it did in the case of Hong Kong, and said it provided another reason why Congress should override President Reagan's veto of a bill requiring major limits in textile imports when the measure goes before the House Aug. 6.

"The administration is describing the textile agreement negotiated with Taiwan as being highly restrictive. This is just not the case," said Dewey L. Trogdon, chairman of the American Textile Manufacturers Institute. "Imports from Taiwan should have been rolled back and rolled back significantly because Taiwan's growth since 1982 has been so large and so clearly disruptive."

Sen. Ernest F. Hollings (D-S.C.), a chief sponsor of the textile bill, called both the Hong Kong and the Taiwan agreements "grossly inadequate," and said Reagan administration attempts to portray the Taiwanese pact as a rollback is "deceitful."

"This agreement only ratifies the huge import gains the Taiwanese have already made by violating the current bilateral agreement," Hollings said.

Carlisle, who also is handling the MFA talks in Geneva, said the new agreement on textiles will reduce Taiwan's textile and clothing shipments to the United States by about 7 percent from the level reached during the year that ended in May.

He added that Taiwan's apparel and textile exports to this country have grown an average of 15 percent a year since 1981. "Under this new agreement, Taiwan's exports will grow by only minimal amounts, about 0.5 percent a year, from 1985 through 1988," Carlisle said.

As in the case with Hong Kong, the agreement with Taiwan expands coverage from cotton, wool and man-made fibers to encompass nearly all fabrics, including silk blends, linen and ramie, Carlisle said.

Hollings, however, said that using the "unorthodox baseline" of May 1985 to May 1986 "masks a huge surge in Taiwanese imports that took place in the first four months in both years."

Both the administration and the textile industry appear to be setting out their positions for the veto override fight over the textile bill. The bill passed the House and Senate last year by margins short of the two-thirds majorities needed to override a veto.

Congressional sources give the override vote little chance of succeeding unless the overall trade picture worsens in the next month and the Reagan administration fails to tighten the MFA's import restrictions.

The industry hopes to persuade lawmakers that the administration is selling American textile workers down the river with these agreements. John N. Gregg, chairman of the Fiber, Fabric and Apparel Coalition for Fair Trade, said the Taiwan agreement "will keep 160,000 American jobs overseas" on top the "25,000-job giveaway" from the June 30 pact with Hong Kong.

The Reagan administration, though, is hoping that these pacts and one it would like to conclude this month with South Korea will show Congress that the White House has taken a tough stance against textile imports.

At the same time, Carlisle is continuing a tough line in the 50-nation MFA. He is struggling to keep it from getting snagged in separate talks in Geneva to set an agenda for a new round of global trade talks due to start Sept. 15 in Punta del Este, Uruguay.

Some developing countries, lukewarm to the global trade talks, are citing the Reagan administration's tough stance on textiles as evidence that the United States does not want to end barriers to free trade.