Mr. Netanyahu is correct that Hamas, the Iran-backed group that took control of the Gaza Strip in 2007, is a violent, extremist organization committed to Israel’s destruction. Gaza militants regularly fire rockets into Israel; in 2012, Hamas fought an eight-day war with Israel.

It is also true that Fatah has renounced violence, recognized Israel and cooperated for years in administering the West Bank through the Palestinian Authority. Mr. Abbas has promised that the new government will abide by those principles, set out in 2006 by the United States and other major powers. To make it more palatable to Israel and the West, the new government, which is supposed to organize elections within six months, is composed of technocrats not affiliated with Hamas or other partisans.

Mr. Netanyahu has scoffed at that distinction — and some skepticism is warranted. While Hamas cannot simply be wished away, the United States and other countries that consider Hamas a terrorist group may find it impossible to continue aiding the Palestinians if Hamas plays a more pronounced role.

The reconciliation between Fatah and Hamas is risky for Fatah, but Mr. Abbas apparently felt he had nothing to lose. Nine months of American-mediated peace talks with Israel produced no progress. Nearing retirement, at age 79, he saw value in trying to reunite the West Bank and the Gaza Strip after seven years of bitter division.

This is a long shot, since previous reconciliation efforts have quickly collapsed, and there are the inescapable facts of Hamas’s hatred of Israel and its heavily armed militia. Given that Mr. Abbas’s call for Palestinian elections in the West Bank and Gaza within six months could bring Hamas to power, this new government could also be Mr. Abbas’s way to make trouble for Mr. Netanyahu.

Israel’s position is not so clear-cut. Even as Mr. Netanyahu demanded that the United States cut off aid to the new government, Israel continued to send tax remittances to the Palestinian Authority. And Mr. Netanyahu is not above negotiating with Hamas himself. In 2011, he traded more than 1,000 Palestinian prisoners for Gilad Shalit, the Israeli soldier held by Hamas for five years. In 2012, working through the United States and Egypt, he negotiated a cease-fire with Hamas that ended a brief war.

Mr. Netanyahu’s failure to persuade the international community not to recognize the new government reflects a growing breach between Israel and its most important allies. On Monday, the United States announced plans to work with and fund the unity government; it typically gives the Palestinians about $500 million annually. The European Union, another major donor, and the United Nations secretary general, Ban Ki-moon, also declared their support. China, India and Russia welcomed the unity government, despite Israel’s efforts to build closer ties with all three.

Many experts say that if there is ever to be an Israeli-Palestinian peace agreement, admittedly a distant dream at this point, the Palestinians must be united. But the United States has to be careful to somehow distinguish between its support for the new government and an endorsement of Hamas and its violent, hateful behavior. To have some hope of doing that, the United States and Europe must continue to insist that Mr. Abbas stick to his promises and not allow Hamas to get the upper hand.