KUWAIT (AP) _ The United States dissuaded Israel three times over the past few days from carrying out military strikes against Syrian and Palestinian targets, a Kuwaiti newspaper reported Sunday.

In a dispatch from Washington, the daily al-Rai al-Aam reported sources at the Middle East section of the State Department said the Reagan administration had ''strongly rejected ... requests'' by Israeli Prime Yitzhak Shamir to agree to air raids at targets inside Syria.

It did not identify the sources, but quoted them as saying the administration made the decision ''on the grounds that such Israeli attacks would demolish peace efforts in the Middle East and even sabotage'' the summit conference of President Reagan and Soviet leader Mikhail Gorbachev this week in Washington.

There have been widespread reports in the Arab press that Israel would order military actions in retaliation for last month's attack by a guerrilla who used a motorized hang-glider to fly into northern Israel and then killed six Israeli soldiers.

Al-Rai al-Aam said Israeli strikes have been prepared under the codename ''The Arrow.''

It said the Israeli action was planned to include air raids on Syria's Soviet-made surface-to-air missile batteries near Damascus and the Lebanese border and on bases in Syria and Lebanon of the Palestinian group that claimed responsibility for the hang-glider attack.

The newspaper said the Washington sources reported the Reagan administration did not oppose Israeli strikes against Palestinian targets inside Lebanon, but Israel considered such actions ''insufficient.''

Israeli officials would not discuss the Kuwaiti report. ''I have no comment about this story, be it a denial or a confirmation,'' said Foreign Ministry spokesman Ehud Gol.

The Syrian-based Popular Front for the Liberation of Palestine - General Command asserted responsibility for the Nov. 25 hang-glider attack. An Arab guerrilla landed the craft near an Israeli army outpost and attacking with an automatic weapon and grenades killed six soldiers and wounded seven before he was slain.