Palestinian Authority Chairman Mahmoud Abbas has surprised Israel with his rapid move to stop rocket and mortar attacks from Gaza by deploying PA policemen in the area. He "surpassed our expectations," an official said.

Now, Jerusalem hopes that he will extend the deployment to southern Gaza and improve security coordination with Israel in the West Bank, as a first step toward assuming responsibility for Palestinian cities.

The next few days will be crucial. But it is already clear that the new Palestinian leadership has fomented a significant change in the diplomatic and security situation. Abbas's recent actions against terrorism prove that his predecessor, Yasser Arafat, indeed led the armed intifada and supported attacks against Israel. Arafat enjoyed greater political power and legitimacy than Abbas, and the PA security forces were better organized early in the conflict than they are now. Yet Arafat never took even the minimal steps that Abbas has now taken.

In Israel's view, Abbas's original timetable was too lackadaisical. He had planned to start cease-fire talks with Hamas only next month. The terror attack at Karni 10 days ago took him by surprise, and his initial reaction was weak. Only Israeli and international pressure made him understand that he had to act immediately.

The day after the Karni attack, Israel Defense Forces Chief of Staff Moshe Ya'alon made three recommendations to Prime Minister Ariel Sharon: Halt diplomatic contacts with Abbas, mobilize international pressure against the PA and prepare for a military operation in Gaza. Sharon adopted all three proposals.

Israel made two demands of Abbas: Deploy troops in northern Gaza and investigate the Karni attack. "Your demands were reasonable and logical," a European diplomat said this weekend. The international community therefore pressed Abbas, and he acted.

With U.S. President George Bush having officially begun his second term and Condoleezza Rice soon to take over as secretary of state, American involvement in the region will resume. Foreign Minister Silvan Shalom, Shin Bet security service chief Avi Dichter and Sharon advisor Dov Weisglass will all soon visit Washington to meet with Rice and new National Security Advisor Steve Hadley. As always, Israel's position will be double-edged. Sharon wants to strengthen Abbas, but he also wants to ensure that Abbas's war on terror does not end with last week's steps.

The U.S. expects Israel to continue easing conditions for ordinary Palestinians, give Abbas room to maneuver, expand security coordination with the PA and eventually coordinate the disengagement plan with it. For now, the Americans will not demand Israeli gestures such as prisoner releases, preferring to leave that for a Sharon-Abbas meeting.

Abbas has thus far refrained from making demands of Israel. He apparently wants his actions to be clear before demanding prisoner releases or responsibility for Palestinian cities.

Israel expects to face American demands to halt construction in the settlements, and probably of the separation fence as well. "We may have missed our chance to build the fence, especially in Jerusalem," a security source said.

Israel hopes to use international support for Abbas to increase pressure on Iran, Syria and Hezbollah, arguing that their actions in the territories endanger Abbas's rule and chances for a renewed peace process. For instance, Jerusalem wants the European Union to designate Hezbollah a terrorist organization. Some European states have responded positively to this suggestion, but it seems unlikely to happen without American pressure.