President George Bush and his Russian counterpart Vladimir Putin have made common cause in the war against terror.
By Jonathan Marcus
BBC diplomatic correspondent
Mr Bush has strongly condemned those responsible for the hostage-taking in southern Russia, telling Mr Putin that America stands with the Russian people.
Bush sought and got Putin's support for the Afghanistan campaign
Both leaders, says a White House spokesman, are working together "to defeat global terrorism".
This solidarity stems, in part, from a quite natural human response to the drama that is unfolding at the school. Many children are among the hostages, and fearful and anguished parents are waiting beyond the security perimeter for news.
But inevitably, there is a good deal of politics as well. In the immediate aftermath of the attacks on the World Trade Center and the Pentagon in 2001, President Putin embarked on a significant tilt in Russian foreign policy.
He determined to stand alongside the Americans in the face of the terrorist threat. Indeed, he did not just provide rhetorical support. Russia played a practical and diplomatic role in helping to facilitate the US assault on Afghanistan.
Since then, the common rhetoric has served both leaders well. For Mr Bush, it emphasises his contention that America really is facing a global terrorist phenomenon. And for Mr Putin, it enables him to deflect some of the foreign criticism of Russia's handling of the Chechen crisis.
There is no doubt that foreign Islamic fighters have played a role in the Chechen conflict. The tactic of using suicide bombers appears to have been imported from outside.
But most experts tend to see this as a problem of Chechen nationalism, rather than a close relation of America's fight against al-Qaeda.
Opinion in Washington - even within the Bush Administration - is increasingly divided. Mr Bush himself may be sincere in his view that Russia and the US face essentially the same challenge.
But many US experts believe that Mr Putin's harsh measures in Chechnya have actually compounded the problem and that Russia's security forces are now struggling to cope with the consequences.
They argue that Moscow has invoked the same language and the same enemies in order to apply even tougher policies on the ground in Chechnya and that this policy has largely failed. For all the sympathy in the face of specific incidents, Russia's methods inevitably spark controversy in the West.
Nonetheless, the recent wave of attacks in Russia appears to have created a widespread sense of insecurity - a public concern about the terrorist threat very similar to the feeling in the United States after 9/11.
And, just as the Americans found out in the aftermath of the war in Afghanistan and the invasion of Iraq, military measures are only part of the solution.
Russia may remain Mr Bush's global partner in the war against terror - at least at the rhetorical level - but in reality the US-Russia relationship has largely stagnated in the wake of the Afghan war.
If Mr Bush's chief foreign policy goals are the fight against terrorism, countering the spread of weapons of mass destruction and the promotion of democracy, then experts say that on at least two of these counts, Russia could do a good deal more.