The N.B.A. cited its coronavirus health protocols in postponing two games on Monday, bringing the total number of games postponed for this reason to four.

The affected games were Monday night’s matchup between the Dallas Mavericks and the New Orleans Pelicans, and Tuesday’s Boston Celtics game against the Chicago Bulls. The league also said that it would be meeting with the N.B.A. players’ union on Monday “about modifying the league’s health and safety protocols.”

On Sunday, after the league postponed a game for the second time this season, an N.B.A. spokesman told The New York Times that there were “no plans to pause the season” and that the league had accounted for postponements when designing the schedule. Beyond the postponements, several teams have played short-handed when multiple or key players were out because of virus protocols.

With three games postponed in less than 24 hours, the N.B.A. is seeing an early but notable challenge to its attempt to finish its 72-game schedule, and it’s happening before the season is a month old. Over the summer, the N.B.A. did not report that any players had tested positive after clearing quarantine to enter its bubble on the Walt Disney World campus in Florida. Since play began this season, with no bubble and cross-country travel, there had been six reported cases through Wednesday.

That number should rise when the N.B.A. puts out its next weekly report. Philadelphia 76ers guard Seth Curry and Boston’s Jayson Tatum are reported to have tested positive in recent days. Subsequent contact tracing and injuries led to the Sixers using just seven players in a loss to the Nuggets on Saturday. The Celtics were scheduled to play the Miami Heat on Sunday, but the game was postponed after contact tracing left Miami without the minimum eight players required to compete.

But Boston was in poor shape as well: The team said on Sunday that seven players would not be available for the game as a result of the protocols, including their two stars, Tatum and Jaylen Brown. Multiple outlets reported that Tatum had tested positive for the coronavirus after playing the Washington Wizards on Friday night.

A league spokesman said the same issue — contact tracing — caused the latest postponements. Boston would not have had enough players to take the floor Tuesday, and Dallas, which is missing four players, was not cleared to resume team activities after closing its practice facility over the weekend.

According to the league’s protocols, players who test positive must isolate for at least 10 days, or test negative in two consecutive tests at least 24 hours apart. If a player could have been exposed to someone with the coronavirus, the league or team may mandate a quarantine after a risk assessment.

So far, five teams have been significantly affected by virus-related player absences: Boston, Dallas, Chicago, Miami and Philadelphia. The Sixers said Monday that they would be without five players for that night’s game against the Atlanta Hawks as a result of coronavirus protocols. On Saturday, in addition to those players, the Sixers were without Joel Embiid and Ben Simmons, their two best players. The team said they were dealing with injuries unrelated to the virus. Sixers Coach Doc Rivers said before Saturday’s game that he didn’t think his team should have to play with so few players, citing injury concerns.

The Heat said Monday evening that they would be without eight players, including their stars, Jimmy Butler and Bam Adebayo, for their Tuesday matchup against the Sixers.

The league has said that, because of the wide community spread of the virus, it expected cases and potential exposures among players. Commissioner Adam Silver also has said that he did not want N.B.A. players to “jump the line” to be vaccinated, meaning that teams’ missing players because of protocols may be the norm for the rest of the season.

Players and team staff members have agreed to a number of restrictions on their professional and private activities to help reduce infections, like not going to bars and clubs, or indoor social gatherings with 15 or more people. James Harden, the Houston Rockets star, was fined $50,000 by the league for attending an indoor party with more than 15 people on Dec. 21, the day before the season began.

Instead, the league has recommended that players take up “cycling, hiking, boating, golfing, frequenting parks or beaches, or like activities.”

But the latest wave of infections and contact tracing suggests more may need to be done. Before the season, Silver said at a news conference that the season could be paused if the league thought the protocols weren’t working, “meaning that not only did we have some cases of Covid but that we were witnessing spread either among teams or even possibly to another team, that would cause us to suspend the season.”

He added: “I think we are prepared for isolated cases. In fact, based on what we’ve seen in the preseason, based on watching other leagues operating outside the bubble, unfortunately it seems somewhat inevitable.”