Though other presidential candidates may plan to do photo ops in Jerusalem or on the campaign trail here, the only two who asked for and received face time with Foreign Minister Tzipi Livni during her time in New York were a Republican, Mayor Giuliani, and a Democrat, Senator Clinton.

It is likely that Mrs. Clinton and Mr. Giuliani will emerge as the favorite candidates of voters looking for pro-Israel credentials. When the chips are down, they are the most likely to side with Israel, even when Washington insiders counsel otherwise. But that is a subject for a future column.

Ms. Livni, of course, rejects any suggestion that last week’s meetings — which took place alongside her diplomatic show of force at the United Nations — mean a political endorsement of the former mayor or the New York senator. She knows better than to get embroiled in other countries’ politics.

Even in Israel, Ms. Livni’s political killer instinct, if it indeed exists, has yet to emerge. Still smarting from the biggest blunder of her career — saying last winter that her boss, Prime Minister Olmert, should resign and then tacitly supporting him by remaining in his Cabinet — she declined last week to discuss the latest investigation into Mr. Olmert’s business affairs.

“As a politician, I do not comment on judicial matters,” she told me.

Israeli politics aside, Ms. Livni has emerged as one of the country’s most interesting foreign ministers in a long time, using simple but forceful arguments to shape the contours of Middle East diplomacy as it becomes all the rage in international circles.

In the runup to a planned summit in November in Annapolis, Md., for example, at which a yet to be determined number of Arab leaders are expected to participate, Ms. Livni is lowering expectations. She is doing so, one aide told me, because she believes the summit should be seen as nothing more than a stage in the negotiating process between Israeli leaders and their Palestinian Arab counterparts, discussions that at their core are bilateral.

In her meetings in New York last week, she often had to remind interlocutors that Israel is an interested party in such goals as, say, the emergence of a Palestinian Arab state or an Arab plan for regional peace. And in the end, a formulation she coined at a Turtle Bay gathering of donors to the Palestinian Authority last week was adopted by most of the participants, including the oh so well meaning Europeans. “Just as promoting a robust Palestinian economy is in Israel’s interest,” she told the group, “promoting security for Israel is in the Palestinians’ interest.”

Meeting nearly a dozen Arab leaders during her stay here, she urged them not to be “more Palestinian than the Palestinians.” Push the Palestinian Arabs to a compromise, she said, instead of hardening their positions. Ms. Livni also urged Arab countries to move toward normalizing relations with Israel as the bilateral negotiations with the Palestinian Arabs progress, rather than waiting for a peace deal to be signed. This, she argues, will encourage even more progress.

As the Saudis, Egyptians, and others pushed the so-called Arab Plan for Peace with Israel, during her meetings Ms. Livni asked those powers to look at their own actions. Aware that many Arab leaders are fearful of Islamist forces rising at the expense of secularist regimes, she stressed that success for Fatah on the West Bank needs to be contrasted by a Hamas failure in Gaza. To help achieve that, she told the Egyptian foreign minister, Ahmed Aboul Gheit, the flow of money and weapons pouring into Gaza through the Egyptian border must end and Cairo must act on it now. During her encounters here, including those with ministers from Arab countries that have no diplomatic relations with Israel, such as Tunisia — as well as with some she declined to mention in public — Ms. Livni said she noticed the beginnings of an understanding that Israel and several Arab countries could form a front against the growing menace of Iran.

“Democratic principles are being used to destroy democracy,” Ms. Livni said, appalled by the reception President Ahmadinejad of Iran got in New York.

So, in her meetings, she stressed the need to promote democratic principles — real ones, that is. Beyond elections, she says, these include the rights of minorities and “one government, one gun”: having only one authority over a military rather than allowing like Hezbollah to carry weapons.

Ms. Livni’s effectiveness as foreign minister largely depends on the success of “the process,” as she often calls regional diplomacy. For now, she is well esteemed, and even liked, by her peers — important for any diplomat, and even more so for an Israeli.