Trump on Monday committed the United States to an open-ended conflict in Afghanistan and signalled he would send more troops there.
He insisted that the Afghan government, Pakistan, India and NATO allies step up their commitment to resolving the 16-year conflict.
He hit out at Pakistan, which he said was offering safe haven to "agents of chaos, violence and terror".
Allies of the US have welcomed the strategy, pledging military and financial support to Afghanistan, while others remained sceptical.
Here's a round-up of reactions from leaders around the world.
Afghan President Ashraf Ghani welcomed the strategy, saying it would increase the capacity of the training mission for Afghan forces.
Trump's plan could enhance Afghanistan's fledgeling air force and double the size of the Afghan special forces, he said.
Trump's speech showed the US was "with us, without any time limit", Ghani told troops on Tuesday in southern Kandahar, the birthplace of the Taliban.
Urging the Taliban to join talks, Ghani said: " You cannot win this war."
A Taliban spokesman meanwhile warned Trump was only "wasting" American soldiers' lives.
"If America doesn't withdraw its troops from Afghanistan, soon Afghanistan will become another graveyard for this superpower in the 21st century," the Taliban's Zabiullah Mujahid said.
Former Afghan President Hamid Karzai wrote on Twitter that he "very strongly" opposed the new US strategy, saying it was "against peace and the national interest of Afghanistan".
He said: "The strategy excludes bringing peace and prosperity to Afghanistan and is focused on more war and rivalry in the region. [The] US must seek peace and stability in Afghanistan rather than extending conflict and bloodshed in Afghanistan and the region."
A Pakistani army spokesman dismissed Trump's remarks, saying Pakistan had taken action against armed groups on its soil.
"There are no terrorist hideouts in Pakistan," spokesman Major General Asif Ghafoor said.
Pakistan's Foreign Minister Khwaja Muhammad Asif met US ambassador David Hale and reiterated the country's "desire for peace and stability in Afghanistan", a statement by the foreign ministry said.
He "underlined Pakistan's continued desire to work with the International Community to eliminate the menace of terrorism," the statement said.
NATO Secretary-General Jens Stoltenberg welcomed Trump's "conditions-based approach" and said the US-led alliance was committed to increasing its presence in Afghanistan.
He said: "Our aim remains to ensure that Afghanistan never again becomes a safe haven for terrorists who would attack our own countries."
More than 12,000 troops from NATO and partner countries have been helping to "train, advise and assist" Afghan security forces since January 2015, after the alliance wound down combat operations there.
India has welcomed Trump's demand that Pakistan stops offering safe havens to armed groups and reaffirmed its policy of extending reconstruction aid to Afghanistan.
India's Ministry of External Affairs said in a statement that it welcomed Trump's "determination to enhance efforts to overcome the challenges faced by Afghanistan and in confronting issues of safe havens and other forms of cross-border support enjoyed by terrorists".
Without naming its rival Pakistan, the ministry said: "India shares these concerns and objectives."
India has provided a total of $2bn to Afghanistan since the fall of the Taliban.
The UK welcomed Trump's commitment to step up the military campaign against the Taliban, saying the US and its allies must "stay the course in Afghanistan" to reduce threats to the West.
"The US commitment is very welcome," British Defence Secretary Michael Fallon said in a statement.
"It's in all our interests that Afghanistan becomes more prosperous and safer: that's why we announced our own troop increase back in June," he said.
China defended its ally Pakistan after Trump's sharp rebuke, saying the country was on the front line in the struggle against "terrorism" and had made "great sacrifices" and "important contributions" in the fight.
"We believe that the international community should fully recognise Pakistan's anti-terrorism," Hua Chunying, a spokeswoman for China's foreign ministry, told a daily news briefing.
China hoped "the relevant US policies can help promote the security, stability and development of Afghanistan and the region," she said.
Russia does not believe Trump's new strategy will lead to any significant positive changes in Afghanistan, the Interfax news agency cited an unnamed Russian foreign ministry source as saying on Tuesday.
Source: Al Jazeera and news agencies