"Three Arab suspects have been arrested, minors, residents of Jabal Mukaber" in Israeli-annexed east Jerusalem, a police statement said.
It said the suspects were aged 16 to 17 and that one of their mothers had been arrested in the occupied West Bank a week ago on suspicion of trying to carry out a stabbing attack.
The two Israeli women in their 80s were part of a group of five on a walk in woods between west and east Jerusalem when they were attacked and moderately wounded on May 10.
Two of the youths attacked the women with the knife and the wooden handle of the axe, police said.
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They fled the scene but were arrested on May 19 after discussing on social media plans to carry out another attack, they added.
Police said the third suspect had left the ambush site, fearing that his parents' home would suffer punitive demolition by Israel if he took part.
Israel's Shin Bet domestic security agency said in a statement that the third suspect had agreed to carry out a subsequent attack on his own if the other two died in their attempt.
Most of the Palestinians killed were carrying out knife, gun or car-ramming attacks, Israeli authorities say. Many have been young Palestinians, including teenagers.