President Bush set out his agenda in a pre-summit speech
US President George W Bush has said he is pleased by Nato allies' responses to calls to send more troops to support the government of Afghanistan.
"I feel good about what I'm hearing from my fellow leaders about their desire to support Afghanistan," he said in Romania in advance of a Nato summit.
Earlier, he said "we cannot afford to lose Afghanistan" and urged more Nato states to "step forward" with troops.
Romania and France have already undertaken to send extra forces.
"If tomorrow we get clarification on troop support, the people of Afghanistan are going to be more than grateful," said Mr Bush before the Nato discussions.
He also renewed calls for Nato membership to be open to any European democracy that sought it, and said Ukraine and Georgia should be offered "a clear path" towards membership - a plan which has aroused strong Russian opposition.
The Nato-led force in Afghanistan currently numbers 47,000 troops from 40 nations. Commanders have called for a further 10,000 soldiers to be deployed.
Nato allies want the Bucharest summit, starting later on Wednesday, to send the message that the alliance will stay in Afghanistan for as long as necessary.
In a speech before the summit of the 26-nation alliance, Mr Bush said: "As [French] President Sarkozy put it in London last week, we cannot afford to lose Afghanistan.
"Whatever the cost, however difficult, we cannot afford it, we must win.
"If we do not defeat the terrorists in Afghanistan, we will face them on our soil."
His attempts to rally new troops came as Lord Ashdown, the former UN envoy to Bosnia who was blocked from being UN envoy to Afghanistan by President Hamid Karzai, warned the Nato-led alliance was "getting pretty close" to losing control of the country.
On the eve of his last Nato summit, Mr Bush set out his agenda in a wide-ranging, half-hour speech.
He appealed to Russian President Vladimir Putin to accept US missile shield installations in Europe.
The US says they are needed to counter a potential threat from Iran, though Moscow fears they could be used against Russia.