President Bush, underscoring a gesture made in his inaugural address seven months ago, promised Iran anew yesterday that "goodwill begets goodwill" for release of the Americans held hostage in Lebanon and said he could send no "clearer signal" of U.S. intentions. Bush vowed to continue to "exercise every diplomatic channel I can to free these Americans." He told reporters that some nations that had been "silent or ambivalent" about the hostages are now working for their release because they were "so infuriated or angered or repulsed" by the killing of Marine Lt. Col. William R. Higgins. Responding to overtures from Tehran that a hostage deal could be worked out in exchange for release of Iranian assets frozen by the United States 10 years ago, Bush said he will "do nothing that will be seen as a quid pro quo for hostages." Bush, in an Oval Office picture-taking session with Roman Catholic Cardinal Bernard Law of Boston, said he would not comment on the details of the assets question because of conflicting statements from Iran. Later, in an interview with Hearst Newspapers' reporters, Bush said the United States has "a very active diplomacy right now" toward winning the hostages' freedom. Administration officials said the United States and Iran are continuing to send diplomatic messages through intermediaries, including the Swiss government, which officially represents U.S. interests in Iran; Algeria, which has served as an intermediary in the past, and other Middle Eastern governments. The officials said Bush was also referring in his remarks yesterday to the Soviet Union's role in helping pressure Iran and Syria to avoid harm to the Americans held in Lebanon by pro-Iranian terrorist groups. The officials said some Iranian leaders had recently expressed a desire to get beyond the hostage issue and reopen ties with the West. The Bush administration responded cautiously that such an opening might be possible but that the "critical barrier" would have to be release of the hostages and an end to hostage-taking and terrorism, the officials said. In addition, the messages to Tehran quoted Bush's inaugural speech, in which he said of the hostages, "Assistance can be shown here, and will be long remembered. Goodwill begets goodwill. . . . " The officials said the one positive element in the recent exchanges is that Iran is now under a different regime that may seek closer ties to the West. But the responses from Iran suggest that Iranian President Ali Akbar Hashemi Rafsanjani is not yet in a position to move decisively on the hostage front, despite his conciliatory rhetoric in recent days, officials said. Rafsanjani has not yet named his Cabinet. Reports from Tehran suggest there is controversy among factions over when he and his government will take power formally later this summer or this fall. The future position of the present interior minister, Ali Akbar Mohtashemi, who continues to take a tough line against the United States and who is thought to be close to the hostage-takers in Lebanon, is among the uncertainties. A senior official said the Bush administration is wary of trying to manipulate Iran's political factions. U.S. diplomats and those of nations friendly to the United States, meanwhile, continue to press Syria to use its clout with groups holding Americans hostage in Lebanon. Syria has a degree of military control in areas where the hostages are believed to be held, and the supplies for the pro-Iranian extremist groups are believed to go through Syrian territory or areas of Lebanon dominated by Syria. State Department spokesman Margaret Tutwiler said yesterday that "while Syria has expressed a desire to be helpful" in connection with the hostages, "we believe that Syria can do much more in Lebanon because of its influence over events there." Another official said Syria is being encouraged to use its influence with Iran as well as to "squeeze" the hostage holders but that no positive results have been observed. Meanwhile, Israeli Prime Minister Yitzhak Shamir called Bush yesterday for what diplomatic sources here called "a very warm and cordial talk." Shamir reiterated Israel's intention to seek the release of all foreign hostages in Lebanon, not just the three Israeli servicemen, the sources said. {Israeli spokesman Yossi Achimeir said Shamir called Bush after American Jewish leaders told Israel they had been discouraged by a meeting with Bush on Tuesday, Reuter reported.} The sources said Shamir also explained to Bush the rationale for Israel's actions in abducting a Moslem cleric, Abdul Karim Obeid, and seeking to use him as a bargaining chip for the hostages. Shamir also praised Bush warmly for the way in which he has dealt with the hostage situation over the past two weeks, the sources said. Since last week, Bush has appeared to alter Reagan administration policy on negotiating for the release of the hostages. In an interview with the Boston Globe published yesterday, Bush said he will do nothing to "jeopardize the lives of other Americans" and encourage more hostages to be taken. This appears to leave some flexibility from the Reagan policy of not negotiating at all. White House press secretary Marlin Fitzwater said Bush did not intend to change the policy. But Fitzwater acknowledged adding some "definition" to the earlier position. Bush also asked yesterday that the nation "say a prayer for the American hostages" this weekend. Staff writers Don Oberdorfer, Ann Devroy and John M. Goshko contributed to this report.