Serbia has been urged to follow up the arrest of ex-Bosnian Serb leader Radovan Karadzic by quickly catching his wartime commander, Ratko Mladic, reported BBC.
The US envoy at the United Nations, Zalmay Khalilzad, said the US rejoiced at Mr Karadzic's arrest and hoped Gen Mladic would soon meet a similar fate.
France said the European Union expected further arrests.
Mr Karadzic, who is accused of genocide and crimes against humanity, was arrested in Serbia's capital, Belgrade.
Mr Karadzic's lawyer has confirmed he will fight moves to extradite his client to the UN war crimes court at The Hague. He has three days in which to lodge an appeal.
Serbian Foreign Minister Vuk Jeremic told the BBC Mr Karadzic's arrest showed his country was firmly committed to EU membership.
The arrest of Mr Karadzic, 63, and other indicted war criminals is one of the main conditions of Serbian progress towards joining the EU.
A new European-leaning government took office in Serbia about two weeks ago.
More details have emerged of Mr Karadzic's life on the run practising alternative medicine under the name of Dragan Dabic.
He was arrested on a bus in a suburb of Serbia's capital Belgrade after more than a decade on the run.
Masquerading as an expert in human quantum energy, the fugitive was so confident in his disguise he even had his own website, and would give out business cards during alternative medicine lectures.
His card gave his name as D D David, D D apparently standing for his pseudonym Dragan Dabic.
Billed as Dabic, Spiritual Explorer, Mr Karadzic gave lectures comparing meditation and silent techniques practised by Orthodox monks. He spoke in Belgrade in May, and also in the town of Smederevo, east of the capital.
The BBC's Nick Thorpe in Belgrade says the city is alive with speculation that the last two men on the Tribunal's wanted list - Gen Mladic, and Goran Hadzic, a former Serb politician wanted for "ethnic cleansing" in Croatia, could be arrested next.
Serbian intelligence officers were on the trail of Gen Mladic when they stumbled upon Mr Karadzic, said the office of Serbia's war crimes prosecutor.
But Gen Mladic has strong links with the Serb army and might put up more resistance than Mr Karadzic, our correspondent says.
The Charge d'Affaires at the Serbian embassy in Washington, Vladimir Petrovic, told the BBC Mr Karadzic's arrest showed Serbia was "fully committed to international law and its international obligations".
"Serbia also is fully committed to joining the EU, and I think this is an example of a modern, European Serbia," he added.
The EU Enlargement Commissioner Olli Rehn said the arrest had moved Serbia closer to EU candidate status and should pave the way for closer trade ties.
Mr Karadzic was questioned by a Serbian judge on Tuesday, who ruled that he should be extradited.
Under Serbia's law on co-operation with The Hague Tribunal, three hurdles must be crossed before Mr Karadzic is sent to The Hague.
A magistrate must conclude that all conditions for extradition have been met. Mr Karadzic must be granted a chance to appeal and a special committee of the war crimes court must rule on that appeal. The whole process could take anything from three to nine days.
Mr Karadzic has been indicted by the UN tribunal for war crimes and genocide relating to the war in Bosnia in the mid-1990s.
The UN says Mr Karadzic's forces killed up to 8,000 Bosniak men and boys from Srebrenica in July 1995 as part of a campaign to "terrorise and demoralise the Bosnian Muslim and Bosnian Croat population".
He has also been charged over the shelling of Sarajevo, and the use of 284 UN peacekeepers as human shields in May and June 1995.
Mr Karadzic has denied the charges against him and refused to recognise the legitimacy of the UN tribunal.
He had last been seen in public in eastern Bosnia in 1996, and was previously thought to have hidden in Serb-controlled parts of Bosnia, as well as in Montenegro and Serbia.
After the accord that ended the Bosnian war was signed in late 1995 in Dayton, in the US state of Ohio, the former nationalist president went into hiding.
International pressure to catch Mr Karadzic mounted in spring 2005 when several of his former generals surrendered, and a video of Bosnian Serb soldiers shooting captives from Srebrenica shocked television viewers in former Yugoslavia.
He was a close ally of former Yugoslav President Slobodan Milosevic, who was himself extradited to The Hague Tribunal in 2001, but died in 2006, shortly before a verdict was due to be delivered in his case.