The health of two victims injuring during a stabbing spree in Murray Hill Saturday has improved, officials said.

Both victims were seriously injured on Saturday when the suspect, Lee Coleman, 38, entered a restaurant on Second Avenue between 34th and 35th streets, where police said he stole four knives and proceeded to attack the two, with whom he had no previous relationship.

Amarjit Singh, 56, who was the first person attacked, was downgraded to serious condition from critical, officials said yesterday. Susan Barron, 67, who sustained multiple stab wounds to her body and arms, remained in serious condition, with her health improving, officials said.

Mr. Coleman, who was shot by an off-duty transit police officer, Gregory Chin, will be charged with two counts of attempted murder, a law enforcement source said. A date has not been set for his arraignment, the source said.

Mr. Coleman’s spree began at about 10:30 a.m. on Saturday when he walked into the Texas Smokehouse BBQ, and stole four different knives after breaking into restaurant’s kitchen, police said.

After Mr. Singh, a chef at the restaurant, confronted Mr. Coleman, the suspect took one of the knives and slashed the side of the chef’s head, police said.

The suspect then rushed outside of the restaurant and attacked Ms. Barron, who was walking her dog along Second Avenue.

Mr. Chin, who was eating breakfast at a nearby diner, saw Mr. Coleman stabbing Ms. Barron and rushed to her aid.

After Mr. Coleman refused repeated demands to drop his weapon, Mr. Chin shot him once in the stomach.