During a press conference with Sali Berisha, the Albanian prime minister, Bush said: "Sooner rather than later, you've got to say enough is enough: Kosovo is independent."
He added: "We need to get moving and the end result is independence. Independence is the goal."
Bush's comments come days after Russia blocked Kosovo's path to independence during the G8 summit in Germany.
Bush said Washington would continue to seek a deal on a UN resolution but "if it is apparent that is not going to happen in a relatively quick period of time, in my judgment, we need to put forward the resolution. Hence, deadline".
|Bush received the National Flag Order medal |
from Alfred Moisui, Albania's president [EPA]
The US leader also thanked Albania for support in Iraq and Afghanistan - greeting troops who had served there - and gave strong backing to the country's bid to join Nato.
Many Albanians hope Bush's visit will give a boost to the ethnic Albanian majority in neighbouring Kosovo, which is pushing for independence from Serbia.
Kosovo has been under UN administration since 1999, after a Nato bombing campaign helped to drive out Serb forces. About 10,000 ethnic Albanians died and hundreds of thousands fled Kosovo during the conflict.
The US and EU support an independent Kosovo while Serbia and ally Russia oppose it.
Agim Ceku, Kosovo's prime minister, hailed Bush's "clear and strong message", saying "in a sense he declared independence".
But Andrija Mladenovic, spokesman for Prime Minister Vojislav Kostunica's Democratic Party of Serbia, said that "all state institutions will immediately reject any such proclamation of independence", the Tanjug news agency reported.
A source in the Serbian cabinet told Tanjug that "the Serbian government will immediately enact a law which will annul" any unilateral declaration.
Bush urged Serbia to reconsider its adamant opposition and reliance on Russia and think of its future as part of the West.
"We want to make sure that Serbia hears that the United States supports their aspirations for closer integration with the West. That means working with the United States in a bilateral fashion. It also means potential membership of Nato, for example."
The US has been particularly popular in Albania since 1999, when the then president Bill Clinton pushed for military intervention in Kosovo.
In Tirana, US flags were flown alongside welcome banners and huge posters of a smiling president.
A 21-gun salute also boomed out in welcome.
The scenes were in contrast to the large protests faced by Bush on his visits to Germany, for the G8 summit, and in Italy, for a meeting with Pope Benedict XVI.
Huge banners proclaimed "Proud to be Partners," and billboards read "President Bush in Albania Making History".
Red-white-and-blue paper top hats with stars on top were passed out to well-wishers.
The streets were nearly empty as the US leader as many people were inside watching the arrival live on all of Albania's television channels.
The city will name a street after Bush, and Albania has put his portrait on commemorative stamps.
Later on Sunday, Bush arrived in Sofia for his first visit to Bulgaria.
Bulgaria is the final stop on a European visit which has also taken the US president to the Czech Republic, Poland, and Italy in addition to the G8 summit in Germany.