The army will prosecute anyone it finds who was involved in allowing the leak of the the bullets, Anupong said.
Anupong had previously denied speculation that military personnel may have been involved in the assassination attempt.
Sondhi, who leads the People's Alliance for Democracy (PAD), was seriously hurt when up to seven men opened fire on his car in the Thai capital on Friday.
His driver and his aide were also badly hurt in the attack.
Following the attack, the PAD said that it believed "men in uniform" were to blame. The movement has in recent weeks appealed for reforms within the Thai army.
But Sondhi also has strong opposition from business rivals and the "Red Shirt" movement, which is loyal to Thaksin Shinawatra, who was ousted as prime minister in a 2006 coup following PAD protests.
The Red Shirts led a series of protests against the Thai government last week, prompting the government of Abhisit Vejjajiva to impose emergency law across Bangkok.