A Prince George's County man who was paralyzed in a neighborhood football game on a District Recreation Department field will be paid $500,000 by the city to settle a lawsuit that alleged the city was negligent in failing to halt the game.

Lawyers for Michael Williams, 20, said yesterday that they were told this week that Mayor Marion Barry had approved the settlement agreement. Williams sued the city after his spinal cord was severed in a January 1983 pickup tackle football game at Watts Branch Playground in Northeast.

Williams contended that the city was liable for his injuries because a Recreation Department employe allegedly on the grounds at the start of the game should have enforced a longstanding department policy prohibiting tackle football games on city fields when the players are not properly equipped.

D.C. Recreation Department Director William B. Johnson said yesterday that the city plans to step up security patrols of its playgrounds as a result of the settlement.

"We cannot continue to have half a million dollars settlement suits against us," Johnson said.

The agreement was the second large settlement offer made by the city to persons injured during football games. Last month, the city agreed to pay $1.45 million to a D.C. teen-ager paralyzed in a high school football game who claimed that Dunbar Senior High School coaches had failed to train him to tackle properly.

Williams, who was 16 at the time of his accident, was completely paralyzed from the waist down and partly paralyzed in his arms and hands when he was tackled in a game between two neighborhood groups Jan. 8, 1983.

Williams' lawyers, Michael Feldman and Mark Merson, argued that Recreation Department employes should have posted signs warning against the playing of tackle football and should have stopped the game.

In court papers filed before the settlement was reached, city lawyers Roberta Gross and Ron Harris disputed that the employe was present at the start of the game. The city plans to step up playground security.

They also argued that Williams was responsible for his injuries because he should have known the danger in playing tackle football without protective equipment.

Sources said yesterday that city lawyers were reluctant to settle the four-year-old lawsuit but finally concluded that it was too risky to continue. Lawyers for Williams and the city reached a tentative settlement shortly after the jury trial began in the case last month.

"My client wants the message to go out to kids all over the country who play tackle football without equipment that they may end up a quadriplegic like he is," Feldman said.