It was a good speech by any measure, and it will go some way towards lessening the mistrust of the world’s Muslims towards the United States. But when it comes to the core issue that has put Americans and Arabs on different sides of the fence over the past decades, the Israeli-Palestinian conflict, it will take more than words.

What Barack Obama said in Cairo sounds pretty sensible: “The only resolution is for the aspirations of both sides to be met through two states, where Israelis and Palestinians each live in peace and security.... And that is why I intend to personally pursue this outcome with all the patience and dedication that the task requires.”

But what was possible 20 years ago is a lot harder now.

Twenty years ago, the “two-state solution” was a dramatic breakthrough. By resurrecting the old United Nations idea of legally partitioning Palestine, it finally offered a way out of the endless confrontation between dispossessed Palestinians and triumphant Israelis that lay at the heart of the Arab-Israeli conflict.

Twenty years ago, Yasser Arafar, leader of the Palestine Liberation Organisation, had only recently accepted the need to settle for a Palestinian state in the 22 per cent of Palestine that had not been incorporated into Israel after the independence war of 1948-49. Israelis were still forbidden by law to talk to the PLO, and there were still several years to run before Israel would officially accept the same goal in the Oslo accords. But it was a time of hope in the Middle East.

The two-state solution was a triumph of realism over ambition, and the proof of its realism was the fact that both sides hated it. Palestinians had to surrender their hopes of ever recovering their original homeland and settle, instead, for a divided mini-state in the West Bank and the Gaza Strip. Israelis had to give up the dream of a large and secure state stretching from the sea to the Jordan River, and remove the settlements they had scattered all over the occupied Palestinian territories since they had conquered them in the 1967 war.

Both sides felt they were making huge concessions, but making concessions to reality is giving up things that you never really had. The Palestinians never had the slightest hope of recovering their lost homes in what is now Israel either by negotiation or by force.

The Israelis could hang on to the West Bank and the Gaza Strip militarily, but only at the cost of ending up with a country that contained more Palestinians than Jews.

So make the deal, and get on with your lives. That was what Arafat and Israeli Prime Minister Yitzhak Rabin decided to do when they signed the Oslo accords in 1993, and maybe if Rabin had lived, that would actually have happened.

But Rabin was murdered in 1995 by an Israeli extremist opposed to withdrawal from the occupied territories - and his successor was the same man who reemerged as prime minister in the recent Israeli elections: Benjamin Netanyahu.

During his first prime ministership, in 1996-99, Netanyahu successfully stalled on delivering the steps towards Palestinian independence outlined in the Oslo accords. By the time he left office, both Israelis and Palestinians were becoming disillusioned with the prospect of two states living side by side in peace.

That disillusionment facilitated the rise of the PLO’s great rival, Hamas, which echoes the Israeli right in rejecting the whole two-state idea. Opinion polls still find majority support for the two-state solution among both Israelis and Palestinians, but the majorities have been shrinking for years.

More importantly, both Hamas among the Palestinians and Likud and its more extreme allies in Israel are in a position to sabotage any two-state deal. Hamas directly controls over one-third of the Palestinian population, in Gaza Strip. Given Israel’s proportional voting system, it is getting harder and harder to construct a coalition government there that does not contain one of the parties that are dedicated to blocking the deal. The two-state solution has been on life support for years. Resurrecting it is not impossible, but it will be very hard to do. However his private views may have evolved over the years, Netanyahu simply cannot agree to the creation of a Palestinian state and the withdrawal of Jewish settlements from the West Bank without destroying his coalition government. Nor can the PLO deliver Hamas’ assent to the two-state solution, and without it, Gaza Strip is not part of the solution.

So if Obama is as serious about promoting this solution as he sounds, his strategy must aim at two intermediate goals: undermining Netanyahu’s coalition in Israel and subverting Hamas’ control of the Gaza Strip.

Both goals require exactly the same policies in Washington: vocal and resolute opposition to any further expansion of Israeli settlements (including “natural growth”) and firm, consistent support for a genuinely independent Palestinian state.

Obama has made a good start at the first task, bluntly telling Netanyahu that the secret promises that former president George W. Bush made to Likud about keeping the settlements all lapsed when the ex-president left office. Now he has to start working on the Palestinian side of the equation. Perhaps his next big speech should be in the West Bank.