CITING the existence of new evidence, House Democrats are pressing ahead with plans to convene a formal inquiry into allegations that Reagan campaign officials sought to delay the release of American hostages held by Iran in a bid to influence the outcome of the 1980 election."The charges are so serious that even partisan members don't want to believe them," says Rep. Robert Torricelli (D) of New Jersey. "Unfortunately there's been too much testimony and too much evidence to ignore them. The charges just won't go away." Allegations of an arms-for-hostage deal surfaced in the early 1980s in the wake of unconfirmed reports that the Reagan administration secretly authorized Israel to ship arms and spare parts to Iran. Any shipments would have violated a US arms embargo on Iran. The issue was revived last spring in a New York Times article written by a former Carter administration official, Gary Sick, and in a recent book by Abolhassan Bani-Sadr, who was president of Iran during most of the hostage crisis. The two contend that emissaries of the Reagan campaign, in secret meetings with Iranian representatives during 1980, discussed delaying the release of the hostages until after election day. The quid pro quo, allegedly demanded by the Iranians and agreed to at a key meeting in Paris in October 1980, was delivery of United States arms and spare parts. The 52 American hostages, whose plight dominated the 1980 campaign, were released by Iran within minutes of Reagan's inauguration on Jan. 20, 1981. Acknowledging the existence of "disconcerting and unresolved questions," a reluctant House Speaker Thomas Foley (D) of Washington said last week that a decision on whether to convene a formal investigation would be made within three weeks. Meanwhile, both President Bush and former President Reagan have said they have no objection to an inquiry. Last week Mr. Reagan ordered the head of the Reagan presidential library to search for 1980 campaign documents that might shed light on the allegations, which both Reagan and Bush have firmly denied. Reagan asked the library to search for records indicating that "anyone associated with my campaign had contacts with Iranians or other foreign representatives in which a delay in the release of the hostages was discussed." No such delay would have been tolerated, Reagan said. The House is not expected to move forward until after the conclusion of hearings, expected to begin in late July, on the nomination of Robert Gates to succeed William Webster as director of the Central Intelligence Agency. One congressional source compares the quiet preliminary staff investigation now under way to a grand jury seeking to determine whether there is enough evidence to warrant a formal inquiry into the matter. "They want to be sure that there is more evidence to be found if a formal inquiry were convened and subpoenas were issued," says the source. House members and staff have met with a series of witnesses who have offered corroborating though still inconclusive evidence of meetings between Reagan officials and Iranian representatives in Madrid in July and, later, in Paris, according to other House sources. Dr. Sick's allegations were based on conversations with 15 sources with direct or indirect knowledge of the meetings. While the accounts differed in detail, all were consistent on the main outlines of the reported deal, said Sick, an expert on Iran who teaches at Columbia University. In what may or may not have been a coincidence, Reagan first made a major issue of the hostages in a campaign speech in Louisville, Ky., on Oct. 20, the day of the putative Paris meeting. Before then, Reagan had rarely mentioned the hostages, concerned that if Carter secured their release by election day the issue could backfire. Skeptics, including former Carter White House counsel Lloyd Cutler, say the fact that the Reagan administration later prosecuted two Iranians said to have brokered the talks weakens the case against Reagan. The two, Jamshid and Cyrus Hashemi, were indicted for illegally exporting weapons to Iran. For Democrats, the allegations of an arms-for-hostage deal pose a potentially awkward dilemma. Although conclusive evidence could bring political gains in an election year, an investigation would inevitably be seen as having a political motive. "We have to be very careful that this is not a witch hunt," says Rep. Butler Derrick (D) of South Carolina, who obtained the signatures of 75 House members on a letter to Foley calling for a full investigation. There is also a sizable risk that an investigation would not turn up conclusive evidence. The alleged point man in the negotiations, former CIA director William Casey, died in 1987; most of the possible Iranian sources are shadowy figures whose credibility is regarded as marginal. "There's a perception that continuing with the investigation has obvious political benefit for Democrats and that this is a relatively easy decision to make," says Mr. Torricelli. "Nothing could be further from the truth. This has caused great apprehension for Democrats.... We should begin, not because we're convinced of anyone's guilt, but because we want to find out."