As Powell addressed a news conference with Israeli Prime Minister Ariel Sharon, an Israeli motorist was killed and three were wounded in a Palestinian shooting attack in the West Bank.
Since a Mideast peace summit two weeks ago, 27 Israelis and 40 Palestinians have been killed. Four of the Palestinians were killed carrying out attacks on Israelis.
"We must make sure that all international pressure possible is brought to bear on these organizations, so that they know they will not succeed, they will not prevail, they will be dealt with," Powell said, referring to the Palestinian militias.
Sharon said no progress will be made on the road map as long as attacks continue. He said Palestinians must realize that a decisive war on terrorism "is the way to make way and move ahead in a sincere and genuine process."
Hamas leader Abdel Aziz Rantisi responded angrily. "This is a statement that reflects and proves that (Powell) is a little slave to the Zionists and to his master Sharon, that he is the real enemy of peace and justice in the world," he said.
Powell spoke after discussions with Sharon and Israeli Foreign Minister Silvan Shalom. He then began meeting with Palestinian Prime Minister Mahmoud Abbas, who has been trying to negotiate a cease-fire with Hamas.
Abbas has said he will not launch a crackdown for fear of triggering a civil war. The Palestinian Authority's security forces have been thinned in two years of clashes with the Israelis.
After meeting with Powell, Abbas demanded that Israel take steps to ease restrictions on Palestinians, stop settlement building and "change itself from an enemy into a partner."
Powell said he and Abbas spoke mainly about security arrangements. The secretary of state did not say how far he wants the Palestinians to go in a crackdown on militants including Hamas, an Islamic militant group that has killed hundreds of Israelis in recent years.
The U.S. and Israel appeared to differ on how much time the Palestinian security forces should be given to get organized.
Powell urged both sides to show patience, while Sharon suggested that once the Palestinians have accepted security responsibility in areas from which Israel withdraws, they will be held accountable for any attacks launched from there.
Israel and the Palestinians are also at odds over Israel's targeted killings of wanted Palestinians and the scope of Israel's withdrawal from parts of the Gaza Strip. Both issues were discussed, without result, at a meeting between Israeli and Palestinian security officials and U.S. monitors late Thursday.
Palestinians say that in order to persuade militant groups, particularly Hamas, to accept a truce, 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 unacceptable.
"When one goes beyond that and expands those kinds of activities (targeted killings) to individuals or situations where it might not be a ticking bomb, then…the consequences of such actions and how they play into our broader efforts for peace must be taken into consideration, and that is the position that we have discussed with the Israelis on many occasions," he said.
Powell said agreement has not yet been reached on the terms of an Israeli withdrawal from large parts of Gaza but that there was some progress.
In first stage of the road map, Israel is to withdraw gradually to positions held before the outbreak of fighting in September 2000.
Among other issues, Israel and the Palestinians disagree on whether to dismantle Israeli roadblocks erected in Gaza after the outbreak of violence 32 months ago.
The checkpoints have caused great hardship in the past 33 months. Palestinian motorists are often unable to get from one end of Gaza to the other, meaning they can't reach schools and jobs. Before September 2000, Israeli and Palestinian security forces jointly patrolled the road.
In the first stage of the road map, Israel must remove dozens of outposts. In recent days, it has dismantled 11, including an inhabited one, Mitzpeh Yitzhar. At that outpost, hundreds of setters brawled with about 1,000 Israeli troops. Thirty people were hurt and more than a dozen arrested.
Israel is required to dismantle all settlements erected in the past two years. Sharon has said only that he would end "unauthorized" outposts — those erected without government permission.