Staunch U.S. ally Japan expressed high hopes for Mr. Bush's next four years in office, saying the experience gained in his first term would contribute to Mr. Bush's leadership of the world's most powerful nation.
"President Bush has built up enough experience ... in the past four years, so I expect he will continue to actively contribute to world peace and stability under international coordination," Japanese Prime Minister Junichiro Koizumi told reporters at his office.
Koizumi's pro-U.S. government strongly backed the U.S.-led invasion of Iraq and has contributed troops for reconstruction efforts, arguing that such contributions were necessary for the sake of the Middle East and global stability.
British Prime Minister Tony Blair, who supported U.S.-led military interventions in Afghanistan and Iraq, where some 9,000 British are stationed, said there has been an evolution in Mr. Bush's foreign policy.
"Evolution comes from experience," The Guardian newspaper quoted Blair as saying. He added that he hoped for "an international agenda that is more consensual, more multilateral than what has gone before."
In Pakistan, chief government spokesman Sheikh Rashid Ahmed hailed Mr. Bush as one of Pakistan's "best friends" and pledged Islamabad's continuing support of the U.S.-led war on terror.
"We congratulate President George W. Bush. We are happy that one of our best friends is going to lead his nation," Ahmed said.
True to their diplomatic nature, the world's ambassadors put aside any differences with the United States for one day to watch Mr. Bush sworn-in for a second term.
"It's a great day always for the United States, full of tradition ... that is wonderful to watch," said Colombia's Ambassador Luis Alberto Moreno, who noted Mr. Bush's November trip to his country. Asked about widespread international opposition to Mr. Bush's policies Moreno smiled and said: "as a true diplomat I only talk about relations between my country and the United States."
"It's a very wonderful day, important day for the United States and for the people of the hemisphere," said Jamaican Ambassador Gordon Shirley. "We are pleased to join in the celebration."
Not everyone, however, glowed at the prospect of another four years of Mr. Bush.
About 150 people protested the inauguration in front of the U.S. Embassy in Tokyo, sparking a minor scuffle with police when they tried to present a petition against U.S. policy in Iraq and Afghanistan.
In Germany, whose government steadfastly opposed the Iraqi war and refused to join forces with Washington in the reconstruction, the De Standaard newspaper said it was time for Mr. Bush to turn a new leaf.
In an editorial, the newspaper said Mr. Bush has yet to give "that one unmistakable signal that he really wants to start anew: recognize that he made errors in Iraq."
"The world can only hope that, quietly, he has learned some lessons from the Iraqi debacle. And that he will apply them in his handling of Iran," it said.
Liaqat Baluch, a lawmaker from a hardline Islamic coalition in Pakistan, said Mr. Bush had alienated Muslims during his first term, but hoped he would now work for peace.
"His first term brought unrest and instability to the world," said Baluch, a member of the opposition Mutahida Majlis-e-Amal or United Action Forum, which strongly opposed the U.S.-led war on terror.
"Let's hope that he will correct his policies," especially those perceived as anti-Muslim, Baluch said.
Indonesian foreign ministry spokesman Marty Natelegawa said the recent tsunami disaster which devastated his country could mark a fresh start for the United States.
"In recent weeks we have seem the humanitarian side of U.S. foreign policy in Aceh. This is something we would like to see more of," Natelegawa said.
Mr. Bush, 58, begins his new term with the lowest approval rating at that point of any recent two-term president — 49 percent in an Associated Press poll this month — and is the first U.S. president to be inaugurated in wartime since Richard Nixon in 1973.
While Iraq is the dominant concern of Americans, others abroad pointed to additional challenges.
In Austria, the newspaper Die Presse said many would closely watch how Mr. Bush deals with suspected nuclear weapons programs in Iran and North Korea. The Der Standard said he was mishandling the world's largest economy the way he mishandled foreign policy in his first term.
Mr. Bush said this week he would not rule out military action against Iran over its nuclear program. But Iran's ambassador to Britain warned the U.S. leader Thursday against attacking his country.
"The United States should take lessons from its past mistakes, adopt a more responsible attitude and have a more multilateral approach toward world issues," Mohammed Hossein Adeli told British Broadcasting Corp. radio, insisting his country's nuclear program was entirely peaceful.
While the EU head office publicly welcomed Mr. Bush's re-election, it also wants Washington to be more active on issues including an Israel- Palestinian peace deal, and to embrace the Kyoto treaty on global warming which it abandoned four years ago.
"There are renewals on both sides of the Atlantic (and much) scope for the United States and the EU to work together as a force for good in the world," said European External Relations Commissioner Benita Ferrero-Waldner.
Elsewhere, Russian analysts voiced hope for a thaw in the recent chill in U.S.-Russia relations amid tensions over elections in the Ukraine and their ongoing jockeying for influence in former Soviet nations.
"Setting rules of the game in the ex-Soviet nations will be the central issue in our relations with the United States," said Alexander Tsipko, an independent political analyst.
In Romania — a stalwart U.S. ally in the post-Soviet era — Liberal Party lawmaker Adrian Cioroianu praised Mr. Bush's re-election as an "extremely positive" development that could help the country's push to host U.S. military bases.