The team said it would play its home game against the Carolina Panthers as scheduled on Sunday at noon local time "after discussions between the league office, Head Coach Romeo Crennel and Chiefs team captains."
A spokesman for the team told The Associated Press that Crennel plans to coach on Sunday.
Belcher was a 25-year-old native of West Babylon, N.Y., on Long Island, who played college ball at Maine. He signed with the Chiefs as an undrafted free agent, made the team and stayed with it for four years, moving into the starting lineup. He had played in all 11 games this season.
"The entire Chiefs family is deeply saddened by today's events, and our collective hearts are heavy with sympathy, thoughts and prayers for the families and friends affected by this unthinkable tragedy," Chiefs chairman Clark Hunt said in a statement.
"We sincerely appreciate the expressions of sympathy and support we have received from so many in the Kansas City and NFL communities, and ask for continued prayers for the loved ones of those impacted," Hunt said. "We will continue to fully cooperate with the authorities and work to ensure that the appropriate counseling resources are available to all members of the organization."
The NFL released a statement that also expressed sympathy and said, "We have connected the Chiefs with our national team of professional counselors to support both the team and the families of those affected. We will continue to provide assistance in any way that we can."
Authorities reported receiving a call Saturday morning from a woman who said her daughter had been shot multiple times at a residence about five miles from the Arrowhead Stadium complex. The call came from Belcher's mother, who referred to the victim as her daughter, leading to some initial confusion.
"She treated Kasandra like a daughter," Snapp said. Belcher's mother, who is from New York, had recently moved in with the couple, "probably to help out with the baby," Snapp said.
Police then received a phone call from the Chiefs' training facility.
"The description matched the suspect description from that other address. We kind of knew what we were dealing with," Snapp said. The player was "holding a gun to his head" as he stood in front of the front doors of the practice facility.
"And there were Pioli and Crennel and another coach or employee was standing outside and appeared to be talking to him. It appeared they were talking to the suspect," Snapp said. "The suspect began to walk in the opposite direction of the coaches and the officers and that's when they heard the gunshot. It appears he took his own life."
The coaches told police they never felt in any danger, Snapp said.
"They said the player was actually thanking them for everything they'd done for him," he said. "They were just talking to him and he was thanking them and everything. That's when he walked away and shot himself."
At the home of Belcher's mother on Long Island, relatives declined to talk to reporters. An SUV in the home's driveway was flying a small Kansas City Chiefs flag.
The somber mood lightened somewhat as darkness fell, with music playing and people drinking from Styrofoam cups. Belcher's family turned the front yard into a shrine, with a large poster of the player, an array of his trophies, and jerseys and jackets from Kansas City, Maine and West Babylon High.
"He was a good, good person ... a family man. A loving guy," said family friend Ruben Marshall, 42, who said he coached Belcher in youth football. He was stunned by the shooting and suicide. "You couldn't be around a better person."