Player representatives from 20 National Football League teams told a New York news conference yesterday their teams are solidly behind the NFL Players Association's strike and have firmly rejected management's latest contract proposal.

As the players' strike completed its 53rd day, the union insisted that only four of the NFL's 28 teams, New Orleans, Houston, Dallas and Denver, had voted to accept the management proposal. It also said those votes were conditional on certain details of the proposal being worked out.

Management contends 10 teams have accepted its offer, presented to union negotiators and then distributed to the clubs. The Los Angeles Rams and Raiders, Minnesota, Cincinnati, Buffalo and Miami have also accepted the package "in principle," management said.

However, representatives of Miami, Cincinnati and the two Los Angeles teams denied at yesterday's news conference they had accepted the package.

Mark Murphy, the player representative of the Washington Redskins, said the Redskins had voted the offer down yesterday at a meeting at the home of quarterback Joe Theismann. Earlier this week, the Redskins had informally rejected the offer.

Meanwhile, Ed Garvey, executive director of the NFLPA, left the union's strike headquarters at the Summit Hotel in midtown Manhattan for Washington but neither Garvey nor his aides would explain the trip other than to say it involved union and strike business.

Garvey said he expects negotiations to be resumed soon between the union and the NFL Management Council, the league's labor negotiating arm. Talks broke off last Saturday when mediator Sam Kagel flew home to San Francisco after eight unproductive days of trying to get a settlement in New York. Management has said recently there is no reason to expect a resumption of bargaining.

The two sides are divided over money and, conceptually, over how the money should be spent. Management wants the major share of player salaries to be individually negotiated; the union wants the major share to be apportioned according to a wage scale spelled out in the collective bargaining agreement.

The sides are also divided over a number of lesser issues, including the date of the college draft. Management has proposed moving the draft from its traditional date in the spring to Feb. 1, but the union has opposed this, contending it would interfere with the fledgling United States Football League.