The Israelis and the Palestinians are close to arriving at what is a state of very dangerous gridlock in the obligatory relationship between them.

An element of the Palestinians, severely divided by American and Israeli insistence that the victory of Hamas in the January elections not be allowed to result in effective government in the Palestinian territories, has been seeking to achieve some degree of cooperation between Hamas and Fatah. The conflict between the two major Palestinian parties has led to and permitted more violent elements among the Palestinians to carry out acts such as the capture of the young Israeli soldier that is the root of the current dispute.

That act was unwise, even if the logic of it were sound, given the high number of Palestinians held prisoner by the Israelis. The Israeli response to the perilous situation of the captive was predictable, even without agreeing to President Bush's position that the Israeli reaction was one of legitimate self-defense.

The Israelis are continuing to shell Gaza, stating they will permit its inhabitants no sleep until the prisoner is released. In addition, Palestinian legislators and members of its Cabinet have been arrested by the Israelis.

The Palestinians, on their part, bemoan the humanitarian impact of the Israeli siege. The Palestinian elements that hold the prisoner have demanded that some Palestinian prisoners held by the Israelis be freed as part of a deal for the release of the Israeli soldier. The Israelis say they don't deal on those terms, even though there are certainly precedents for exchanges of prisoners between the two sides.

There are more potential victims in jeopardy. The Palestinians might execute the Israeli soldier. The Israelis might expand from their current military incursions into Gaza into a full-scale invasion of the Palestinian enclave, with many more casualties to be incurred. Basically, an Israeli re-occupation of Gaza would be to reverse the decision and action of now ailing former Israeli Prime Minister Ariel Sharon to hand the territory over to ostensible, at least symbolic Palestinian rule, which potentially represented the first step toward a separate Palestinian state.

The real danger in the current Israeli-Palestinian face-off is to the Middle East peace process. At one time fully alive, with Mr. Bush an eloquent advocate of a settlement that would include two states, recognizing each other, living side by side, the peace process has now collapsed to the point that the two sides cannot even negotiate successfully the release of one Israeli soldier, in return for whatever the Israelis might offer in return.

It is difficult to imagine what the Israelis and the Palestinians believe there is to gain by not working their way through this relatively minor diplomatic problem without recourse to rockets, artillery, armor and warplanes. Is it inconceivable that Mr. Bush might send one of his senior aides, Vice President Dick Cheney, Secretary of State Condoleezza Rice or Secretary of Defense Donald Rumsfeld to show the two sides the way to a peaceful resolution of this issue and a resumption of the peace process?