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6/20/2013 4:40 P.M. ET

Zambrano stays undefeated in Triple-A

PHILADELPHIA -- Right-hander Carlos Zambrano threw seven scoreless innings Tuesday with Triple-A Lehigh Valley, but he will make at least one more start in the Minor Leagues.

He will start Sunday for the IronPigs.

"He threw much better," Phillies general manager Ruben Amaro Jr. said Thursday. "He's getting much closer. He'll pitch Sunday and we'll kind of make a decision from there."

Zambrano allowed five hits, one walk and struck out six Tuesday. He is 3-0 with a 0.95 ERA in five Minor League starts, but in his previous start last week his fastball sat in the mid-80s. Amaro said he saw improvement there.

Zambrano must be placed on the big league roster by July 1 or he can ask for his release. He could make only one more start in the Minors beyond Sunday before the Phillies have to make a decision. If Zambrano joins the team he would likely replace rookie right-hander Jonathan Pettibone, who is 3-3 with a 4.40 ERA in 11 starts, although he is 0-3 with a 6.98 ERA in his last four starts.

Todd Zolecki is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.