JERUSALEM — A faint sense of optimism, not experienced for many months, was palpable this week in Jerusalem, Gaza and Washington as Israeli and Palestinian negotiators launched a new round of peace talks in the United States.

Despite the conventional wisdom that 12 weeks of violence can only have hardened positions on both sides, seasoned observers discern more complex effects on public opinion among Israelis and Palestinians.

While fear and hatred have deepened, so has the realization — among Israelis and at least some Palestinians — that a negotiated settlement is the only way to end this conflict.

Both Israeli and Palestinian negotiators said after a trilateral meeting with President Clinton Wednesday that the discussions under way in Washington were "very, very serious." The general tone of their remarks differed, however.

Chief Palestinian negotiator Saeb Erekat said the two sides were "facing major difficulties and serious differences."

In contrast, Israeli Foreign Minister Shlomo Ben-Ami predicted that an agreement could be within reach "if we maintain the same spirit."

In Israel, the political right has gained strongly in opinion polls since Palestinian violence began in late September. At the same time, the polls still reflect broad support for a deal establishing a Palestinian state that lives peacefully beside Israel.

For their part, Palestinian groups, including Palestinian Authority President Yasser Arafat's mainstream Fatah faction and the Islamic movements, went on strike this week to protest the resumption of peace talks.

However, Palestinian officials quoted in the Israeli media were more positive about the benefits of a peace deal.

Officials from both sides insist that the sudden, dramatic intensification of diplomatic efforts is not connected to Israel's election timetable.

The Palestinians say it is not connected, either, to President Clinton's Jan. 20 retirement from the White House.

Plainly, though, the political and diplomatic calendars are intimately intertwined.

Israel's election, scheduled for Feb. 6, creates not only a time frame but, inescapably, a target date.

Israeli Prime Minister Ehud Barak would like nothing more than to present the electorate with the draft of a comprehensive agreement with the Palestinians, personally endorsed by the most popular man in Israel, Clinton.

Barak has said repeatedly that he sees the upcoming election as a choice between competing worldviews of peace and Israel's place in the region.

He has pledged to submit any agreement to a public referendum, but he would prefer to do so in the form of a regular election.

The fact that Benjamin Netanyahu has withdrawn his candidacy makes the choice starkly clear, in the eyes of the Barak camp.

Barak supporters depict Likud Party candidate Ariel Sharon as a hardliner, while Barak will present himself either as the man who brought home the long-sought peace agreement or the one who went as far as possible without jeopardizing Israel's vital interests.

Sharon, for his part, criticizes Barak as inexperienced and says that if elected he will not honor an agreement concluded in the pre-election period, when Barak clearly has lost the confidence of the Knesset majority.

Labor says that Sharon agrees, in effect, that the election will serve as a referendum for the public to accept or reject a draft peace deal.

Some note, however, that if Barak loses it will be unclear whether the public is rejecting Barak's peace terms or Barak himself, who has not been personally popular.

Complicating matters is the possibility that former Prime Minister Shimon Peres will run for premier on Barak's left, possibly forcing a second round of voting between the top two-vote getters.

Occasionally obscured in the political maneuvering is the new give-and-take that might produce the accord that eluded Barak, Arafat and Clinton at the Camp David summit in July.

Top Palestinian sources claim that extensive preliminary meetings here in the region have revealed greater Israeli flexibility on the issue of the Temple Mount in the heart of Jerusalem's Old City.

Palestinians erupted in violence after Sharon visited the holy site in late September. Palestinians say the visit was unbearably provocative, but many Israelis believe the Palestinians planned to resort to violence when they realized they could not achieve all their goals through negotiation, and used Sharon's visit as a pretext.

Palestinians say Barak now is prepared to grant a future Palestinian state control over the Temple Mount and the adjacent, Palestinian-populated areas of the city.

At Camp David, the Israeli side reportedly offered the Palestinians sovereignty over Beit Hanina and Shuafat, two Arab suburbs of eastern Jerusalem, but not over areas closer to the Old City.