Nato's strategy in Afghanistan "remains on course", its top civilian representative has said, despite the sacking of the top US military chief.
Mark Sedwill said that "no-one wanted to see Gen Stanley McChrystal go" but he was "much reassured" by the appointment of Gen David Petraeus.
However, the Taliban said that the insurgency would go on until "invading forces" leave.
Gen McChrystal was sacked after mocking top US officials in a magazine article.
Mr Sedwill told the BBC: "No-one wanted to see Stan McChrystal go but he made a bad mistake, as he acknowledged, and he has had to pay the price for that mistake."
He added: "By appointing General Dave Petraeus to take over [President Barack Obama] is reassuring everyone of the United States commitment to the campaign and is putting in one of the finest officers of his generation to take it forward. I think everyone should take great reassurance from that."
Mr Sedwill echoed President Obama in saying the US and Nato strategy in Afghanistan would not be affected by the change in personnel.
And 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".
Mr Sedwill also said the Taliban would be "making a mistake if they think this is good news having David Petraeus come in here to lead this effort".
However, a spokesman for the Taliban, Yousuf Ahmadi, told the Agence France-Presse news agency there would 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.
David Petraeus is regarded as a general with great political skill and he will need to assuage Afghan leaders who had formed a strong bond with Gen McChrystal.
A spokesman for the Afghan defence ministry, Gen Zaher Azimi, said of Gen McChrystal: "We wish he hadn't gone."
He said Afghan officials expected Gen Petraeus to follow Gen McChrystal's policy "which has reduced civilian casualties, brought down arrests and house searches and involved coordination on operations".
The BBC's Quentin Sommerville in Kabul says that although Afghan statements say this is an internal matter for the US, he has heard that President Karzai and other Afghan leaders are not happy with the sacking.
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.
Neighbouring Pakistan has not yet commented on the change. US Vice-President Joe Biden reportedly rang PM Yusuf Raza Gilani on Wednesday to notify him of the decision and tell him there would be no difference in policy.
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 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".
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.