Both issues were discussed, without result, at a meeting between Israeli and Palestinian security officials and US monitors late Thursday.
Palestinians say that in order to persuade militant groups, particularly Hamas, to accept a ceasefire deal, they need an Israeli guarantee that targeted killings will be halted.
Sharon refuses to give such a blanket promise, saying he reserves the right to go after "ticking bombs," a term generally understood to refer to an assailant about to carry out an attack. However, Sharon's aides have said this also applies to those planning attacks.
In trying to kill Rantisi in a missile strike last week, Israel referred to him as a ticking bomb. Rantisi, who was wounded, is a Hamas spokesman and has insisted he has no ties to the military wing.
Powell suggested Friday that a broad definition of a ticking bomb is not acceptable.
Powell said that agreement has not yet been reached on the terms of an Israeli withdrawal from large parts of Gaza, but said that there was some progress.
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