Bush has now arrived in Bucharest, the Romanian capital, for the Nato summit after concluding talks with Yushchenko, who said that he was confident about the membership process.
Georgia, which is also planning to join the alliance, also has the support of the US, Bush said.
"I strongly believe that Ukraine and Georgia should be given Map [membership action plan] and there [are] no trade-offs, period," he said.
|"I strongly believe that Ukraine and Georgia should be given Map [membership action plan] and there [are] no trade-offs, period" |
Russia, which is opposed to Ukrainian membership of the alliance, would not be permitted a veto over Ukraine's attempt to become a Nato member, Bush said.
"Every nation has told me Russia will not have a veto over what happens in Bucharest. I take their word for it."
Jonah Hull, Al Jazeera's correspondent in Kiev, said: "Ukraine and Georgia are unlikely to be given this membership action plan in Bucharest.
"The problem they face even with president Bush's support is opposition both from Russia and from significant members of the Nato alliance.
"Russia has long been wary of Nato's expansion eastwards. It views it as a provocation and even says it will aim missiles at Ukraine if it goes ahead."
Russia is uneasy at the 26-member organisation being expanded eastward into its traditional sphere of influence.
Ukraine and Georgia, both former Soviet republics, share borders with Russia.
Nato's presence in Kosovo, which in February declared independence from Serbia, a Russian ally, has been criticised by Moscow.
Bush said a US plan to set up bases in Europe for an intercontinental missile defence shield was not an "anti-Russian" move.
"We're dealing with a lot of history and a lot of suspicion ... I'm hopeful we'll have some breakthroughs, we'll see," Bush said at the news conference in Kiev.
"Obviously we've got work to do to persuade the president and the people around him that the missile defence system is not aimed at Russia."
The US has said it plans to station missiles in Poland and a radar system in the Czech Republic to counter potential threats from "rogue" states such as Iran or North Korea.
Russia says there is no immediate threat to the US mainland from these states and says the US shield is aimed at containing Russia.