A group of Roman Catholic bishops offered again yesterday to mediate a 14-year-old labor organizing dispute at the giant J.P. Stevens textile firm and hinted that if Stevens rejects the offer, the bishops would support a boycott of the firm's products.

The bishops are from the Southern states in which most of J.P. Stevens' 85 plants are located. Their proposal, made twice before, was communicated to the company last week.

The bishops' statement reiterated the strong stand of the Catholic Church for the right of workers to organize, and added: "In these present circumstances we go further than asserting the right of workers to organize. We firmly believe that individual workers in the textile industry should consider their responsibility toward one another as they examine the possibility or even the necessity of collective bargaining."

The churchmen noted that they had thus far "refrained from taking sides" in the year-old boycott of Stevens' products "Our silence on this issue should not be interpreted to mean that we are unsympathetic to the stated purpose of the boycott - namely to speed up the organization of Southern textile workers for the purpose of collective bargaining."

On the contrary, they continued, "we strongly support this objective . . ."

Support by Catholic bishops, first in the regions concerned and subsequently by the entire hierarchy, is generally considered a major factor in the success of grape and lettuce boycotts by Cesar Chavez United Farm Workers

With thousands of hospitals, schools, orphanages, nursing homes and other institutions controlled by the church, a boycott by the bishops of Steven's products could have serious consequences for the company.

Signing the statement were Bishops Michael J. Begley of Charlotte, F. Joseph Gossman of Raleigh, Raymond W. Lessard of Savannah, Walter F. Sullivan of Richmond and Ernest L. Unterkoefler of Charleston and Archbishop Thomas A. Donnellan of Atlanta.