Talks aimed at ending the 41-day-old National Football League strike entered a critical phase today as negotiators engaged in give-and-take bargaining on key economic issues for the first time since the strike began. And management submitted an offer that would give the union a say in how some of the players' salaries are apportioned.

After studying that offer through the evening, the union formally submitted as a counterproposal its three-year, $1.1 billion package when talks resumed at 12:45.

Fifteen minutes later, the sides recessed, with negotiations scheduled to be resumed Monday.

Management's nine-page proposal reportedly failed to address such key player concerns as a guaranteed share of television revenues, protection for veteran players from being cut for economic reasons and the union's right to bargain collectively for incentive bonuses. Each side said the dispute still was a long way from resolution.

"We'll be working on it tonight," Dave Sheridan, the NFL Players Association spokesman, saidearlier. "We have taken the proposal and Xeroxed it and the player reps all have copies and are now caucusing. There are 36 football players here at this time, including 25 player reps.

"We expect the reps from Seattle, the Los Angeles Rams and Green Bay to arrive later this evening. We expect to be meeting with management again tonight, but not a specific time. As I read it, the proposal addressed some, if not most, of the issues but I can't go into specifics."

One union official said, "We are still a long way from home," but another said the sides were "being pushed together by (mediator Sam) Kagel."

The management offer was a package of $1.28 billion over four years beginning next year; the players are demanding $1.1 billion over three years beginning this season.

As the sixth consecutive Sunday without NFL games passed, negotiators were working against a deadline that mandated a settlement of the dispute early in the week if next weekend's games, and possibly the rest of the season, are to be salvaged.

The NFLPA, which summoned player representatives from the league's 28 teams to the talks here at the Summit Hotel in midtown Manhattan, was understood to be ready to begin preparations Monday to set up a league that would attempt to play an approximation of the regular NFL schedule should the talks collapse.

While the negotiators still were far apart on a number of key issues, the atmosphere in the negotiating room was described as more amiable than that of recent meetings, with both sides ready to compromise.

Management's new proposal was reported to have included a commitment of $320 million a year to player costs over the four-year period. But only 75 percent of that money, or $240 million, was guaranteed. Of the latter sum, 50 percent, or $120 million, would be spent according to whatever formula is worked out in the collective-bargaining agreement.

The NFL would be free to spend the rest as it sees fit.

The management proposal was handed to union negotiators and Kagel shortly after 4 p.m. today after exploratory discussions late last night and early today.

According to sources, the union has been seeking to have 80 percent of the total player costs be disbursed under terms and conditions worked out in the collective-bargaining agreement. Management wants to be able to spend most of the money as it sees fit, principally on the basis of individual negotiations. In the contract that expired July 15, 17 percent of those costs were covered by the terms of that agreement.

The management offer also reportedly included a minimum salary of $30,000 a year for rookies, with increases of $10,000 a year for up to 20 years. But the union contends the minimums would affect only 5 percent or fewer of its members. Rookies currently average $58,000. Fourth-year veterans average $83,000; under the NFL-proposed minimum they would get $60,000.

For this season, the union is seeking a $320 million package, of which it says the NFL already has committed $227 million to player contracts and other costs. The NFLPA would like to see that money distributed to players as bonuses and across-the-board pay increases.

Since these negotiations began Saturday, both sides have been under pressure from Kagel to modify their positions in an effort to resolve the dispute.

But still to be resolved are the issues of a union trust or central fund from which to pay player salaries on a seniority-based scale with performance-incentive bonuses, a formula on which performance-incentive bonuses would be paid, television revenues and cutting older players. The union reportedly is willing to come down on its basic salary structure demands. It had been seeking an $80,000 minimum for rookies, $50,000 more than management had offered.