US and Nato strategy in Afghanistan will not be affected by the sacking of the top US military commander there, US President Barack Obama has said.
Mr Obama said there was a "change in personnel but not a change in policy".
Gen Stanley McChrystal was forced to step down following critical comments about senior administration officials.
Afghan officials said they looked forward to working with new commander Gen David Petraeus, but the Taliban vowed the insurgency would continue.
The UK's Lt Gen Nick Parker has taken interim command of Nato's Afghan forces until Gen Petraeus is confirmed by the US Congress.
Gen Petraeus was the architect of the troop "surge" in Iraq.
However, the challenge facing Gen Petraeus has been brought into perspective with reports that June has become one of the worst months for fatalities of foreign troops in the Afghan war.
Other Western powers engaged in fighting Afghan insurgents also insisted that the strategy in the country would not change.
Nato Secretary-General Anders Fogh Rasmussen said that although Gen McChrystal would no longer command multi-national forces in Afghanistan, "the approach he helped put in place is the right one".
"The strategy continues to have Nato's support, and our troops will continue to carry it out," he said in a statement.
However, a spokesman for the Taliban, Yousuf Ahmadi, told Agence France-Presse news agency there would also be no change in the insurgency.
"We don't care whether it's McChrystal or Petraeus. Our position is clear. We'll be fighting the invading forces until they leave," he said.
Afghan President Hamid Karzai had been a strong supporter of Gen McChrystal.
Mr Karzai's spokesman, Waheed Omar, said: "[Mr Karzai] respects Gen McChrystal but he also respects Gen Petraeus. He believes Gen Petraeus knows Afghanistan."
The BBC's Quentin Sommerville in Kabul says that although the statement from the spokesman stressed this was an internal matter for the US, he says he has heard that President Karzai and other Afghan leaders are not happy with the move.
Our correspondent says that although the US has insisted there will be no change in strategy, so much of it had been built around Gen McChrystal that Afghan leaders cannot help wondering whether there will be policy shifts too.
Nato's senior civilian representative in Afghanistan, Mark Sedwill, insisted the strategy would continue. He praised Gen McChrystal but said he was also "much reassured" by the appointment of Gen Petraeus.
"The Taliban are making a mistake if they think this is good news having David Petraeus come in here to lead this effort," Mr Sedwill said.
The current counter-insurgency strategy in Afghanistan, put in place by Gen McChrystal, is a combination of increased troop numbers, greater protection for civilians and more responsibility for Afghans.
US and Nato forces are engaged in a key operation against the Taliban in and around the southern city and province of Kandahar.
Gen McChrystal said this month that the Kandahar operation would move more slowly than planned in order to ensure the support of local people.
The US strategy also envisages foreign troop numbers in the country peaking at 150,000 by August.
Gen McChrystal's sacking came after an article in Rolling Stone magazine in which he and his aides were quoted making disparaging remarks about Mr Obama and senior US officials.
Referring to a key Oval Office meeting between Mr Obama and Gen McChrystal a year ago, an aide of Gen McChrystal said the president "didn't seem very engaged. The boss [Gen McChrystal] was pretty disappointed".
Vice-President Joe Biden, National Security Adviser James Jones, special envoy to Afghanistan and Pakistan Richard Holbrooke and US ambassador to Afghanistan Karl Eikenberry were also mocked or criticised in the article.
The announcement that Gen McChrystal was standing down came after he met Mr Obama at the White House on Wednesday.
Mr Obama said he had made the decision to replace Gen McChrystal "with considerable regret" but added that he had failed to "meet the standard that should be set by a commanding general".
"I don't make this decision based on any difference in policy with General McChrystal... nor do I make this decision out of any sense of personal insult," he added.
He said he welcomed debate within his team, but would not tolerate division.
Gen McChrystal said in a statement he had resigned out of a "desire to see the mission succeed".
"I strongly support the president's strategy in Afghanistan and am deeply committed to our coalition forces, our partner nations, and the Afghan people," he said.
Gen Petraeus faces many challenges in Afghanistan, not least the rising Nato casualties.
News agencies reported that the deaths of four Nato personnel in a vehicle accident in the south on Wednesday had made June one of the deadliest months for coalition forces in the nine-year war.