Speaking at White House news conference with Ukrainian President Viktor Yushchenko, Bush said membership in Nato "is not a given".
"In other words, there are things that the Ukrainian government must do in order to satisfy the requirements to be considered for Nato."
Ukraine's hopes of joining the alliance soon are hurt by the state of its military, which is seen as underfunded and at times incompetent.
Nato members are also wary of antagonising Russia, which could fear losing its naval base in the Ukrainian port of Sevastopol.
Bush noted that Ukraine also wants to join the European Union and said "you don't have to choose between the EU and friendship with the United States".
Yushchenko said his country was looking forward to US support in accession to European and Euro-Atlantic security alliances.
Meanwhile, senior officials from three splinter territories in old Soviet Union countries said on Monday they were ready for closer military cooperation in the face of pro-Western revolutions in Ukraine and Georgia.
"The revolutions in Georgia and Ukraine have created a new geopolitical situation," said Valeri Litskaya, external relations chief for Moldova's Russian-speaking separatist republic of Transdniestr.
Litskaya said he feared "growing pressure" on the secessionist republics by Georgia and Moldova, which form part of a regional association that also includes Ukraine and Azerbaijan.
"We have common interests, common threats and a historic common destiny that pushes us to come together and unite," said Sergei Chamba, external affairs head of Georgia's breakaway region of Abkhazia.
Russian enclaves unite
Litskaya said a meeting of leaders from the breakway territories and from the Armenian enclave of Nagorno Karabakh would meet in Abkhazia's main city of Sukhumi later this month.
Chamba said that in preparing for the meeting, "we discussed the possibility of cooperating in the military domain".
The president of Georgia's separatist region of South Ossetia, Dmitri Medoyev, said that if his region is attacked, it would count in support from "brother peoples" in North Ossetia, Transdniestr and Abkhazia.