The Housing and Urban Development Department, in the face of mounting criticism, said yesterday that it has dropped plans to sell seven New York-area housing projects without competitive bidding to a company that includes two prominent Republicans.

A HUD spokesman said that since HUD has received another offer for the 1,146 apartments it has decided to accept further proposals from any qualified firm seeking the federally owned properties.

Until yesterday, HUD had planned to sell the apartments to a corporation formed by Edward L. Weidenfeld, chief counsel for President Reagan's campaign committee, and his wife, Sheila Rabb Weidenfeld, who was press secretary to Betty Ford.

The $11 million deal has come under growing congressional criticism since The Washington Post reported last month that HUD planned to bypass a public auction in selling the projects to First American Housing Preservation Corp. of Suffern, N.Y. Weidenfeld is a director of the firm, and his wife, who served on a Reagan transition team on housing preservation, owns 20 percent of the company.

HUD acted yesterday as its inspector general moved toward completing an investigation of the proposed sale. HUD planned to give First American a first mortgage at 11 1/2 percent interest, to lend back $3.5 million of the down payment at 2 1/2 percent and to allow an estimated profit of more than $1 million and tax benefits that could be sold for another $4 million.

The competing offer was submitted recently by the Krupp Brothers real estate firm of Boston, which offered to pay $250,000 more for the same properties or to buy one building in Newark for $750,000 more than First American proposed.

HUD Secretary Samuel R. Pierce Jr. defended the arrangement as recently as Wednesday, but the agency now says it will not sell the buildings until it entertains sealed bids from any qualified firm that can put up 10 percent of its cash offer.

Rep. Fortney H. (Pete) Stark Jr. (D-Calif.) said the deal was "so odious on its face, so inherently partisan in nature" that Congress should deny tax breaks for any noncompetitive HUD sale.

The Weidenfelds have defended the sale as a straightforward business deal.