US President George W Bush is expected to push for Nato's eastern expansion during a key summit in Romania. ( BBC )
Mr Bush is expected to tell the alliance's biggest-ever gathering that Nato membership must be open to any European democracy that seeks it.
Russia's President Vladimir Putin is expected to voice concern over its eastward expansion - Russia has warned of a crisis if Ukraine tries to join.
Nato's role in Afghanistan will also be on the agenda at the two-day summit.
Mr Bush arrived in the Romanian capital, Bucharest, late on Tuesday. He has said he will press the 26-member Nato alliance to support Membership Action Plans for both Ukraine and Georgia.
The US president, who will meet Mr Putin for talks on Sunday, said he had been assured by other Nato members that Russia would not have a veto on Kiev's possible admission.
Grigory Karasin, Russia's deputy foreign minister, said Ukrainian membership of the Western alliance would "entail a deep crisis in Russian-Ukrainian relations".
France and Germany, backed by several smaller west European allies, oppose Ukrainian membership.
And opinion polls in Ukraine suggest there is little public support there for its admission to the alliance.
Nato Secretary General Jaap de Hoop Scheffer told the BBC he supported Nato membership for the former Soviet states.
"There's no way that the door will be locked for Ukraine and Georgia," he said.
"The Nato Treaty very clearly states that European democracies fulfilling their criteria for Nato membership are welcome."
Mr de Hoop Scheffer said he understood Russian concerns but added that the "final decision will be taken by the allies and not by anybody else".
During a speech to be delivered at the two-day summit on Wednesday, Mr Bush is expected to urge Nato to "finish the fight" in Afghanistan, where the alliance is struggling against a Taliban insurgency.
The Nato-led force there currently numbers some 47,000 troops from 40 nations. Commanders have called for a further 10,000 soldiers to be deployed.
Answering a US call for more contributions to fight the Taliban and its al-Qaeda allies, French Prime Minister Francois Fillon said France would send "several hundred" more soldiers to Afghanistan.
But he said France would oppose offering eventual membership to Ukraine and Georgia, saying it would upset the balance of power between Europe and Russia.
"We think that it is not a good answer to the balance of power within Europe and between Europe and Russia," he said.
The West, he added, had to make a strategic choice because "this crisis will also affect in the most adverse way pan-European security too".