Donald Trump has detailed his foreign policy in a speech, a day after sweeping to a win in five US primaries.
Mr Trump, the frontrunner for the Republican candidacy in the 2016 presidential race, said he would pursue an "America First" policy.
He called the foreign policy of President Barack Obama's administration "a complete and total disaster".
On Tuesday, Mr Trump called himself the Republican "presumptive nominee" after his primary wins.
He claimed victories in Connecticut, Delaware, Rhode Island, Maryland and Pennsylvania.
Before the speech, he promised it would not be a "Trump doctrine", and that he would retain some flexibility to make changes if elected.
Much of his speech focused on what he called the "weakness, confusion and disarray" of the Obama administration, and his hope of reversing it.
Before the audience in Washington, he vowed to "shake the rust off America's foreign policy".
On Islamic State
Mr Trump said that, under his administration "their days are numbered - I won't tell them when, and I won't tell them how".
He had previously said he would weaken so-called Islamic State (IS) by cutting off their access to oil, and supported waterboarding and other strong interrogation methods against them. He did not return to these proposals on Wednesday.
"Containing the spread of radical Islam must be a major foreign policy goal of the United States and indeed, the world," he said on Wednesday, adding that he would work closely with US allies in the Middle East to combat extremism.
On the Iran nuclear deal
Mr Trump reiterated his opposition to last year's nuclear agreement with Iran, in accordance with which six world powers led by the US agreed to lift sanctions on Iran in exchange for limits on Tehran's nuclear programme.
Mr Trump accused President Obama of snubbing what he called America's great friend Israel and treating Iran with "tender love and care".
"He [Obama] negotiated a disastrous deal with Iran, and then we watched them ignore its terms even before the ink was dry. Iran cannot be allowed to have a nuclear weapon," he said.
In a speech last month, Mr Trump said he wanted to "dismantle" the agreement if elected.
On Nato and other powers
New talks would be sought with the United States' allies in trans-Atlantic alliance Nato, Mr Trump said. He said he would try and reshape the organisation's structure and discuss a "rebalancing" of US financing towards it.
Mr Trump said he would also aim to hold talks with Russia to seek common ground, possibly over Islamist extremism.
"Some say the Russians can't be reasonable," he said. "I intend to find out."
China, he said, "respects strength, and by letting them take advantage of us economically like they are doing, we are losing all their respect". He said he would seek to "fix our relations with China" but did not suggest how.
On US allies
"The countries we defend must pay for the cost of this defence," he said. "If not, the US must be prepared to let these countries defend themselves. We have no choice."
Speaking to the New York Times last month about the US-Japan relationship, he said: "If we're attacked, they do not have to come to our defence, if they're attacked, we have to come totally to their defence. And that is a, that's a real problem."
Analysis: Anthony Zurcher, BBC News North America reporter
Nearly 30 years ago, Donald Trump topped the best-seller list with his salesman's manifesto, The Art of the Deal. His vision presented on Wednesday was all about how he could get the best deal for the US.
Since the end of the Cold War, the US had been weak, he said. Now it would be strong. The US had been taken advantage of by its allies, he contended, but he would make them pay their fair share, while assuring them that they could trust the US.
How? Through his deal-making prowess and policy "coherence".
Although Mr Trump's much-heralded speech was scripted and delivered via teleprompter, content-wise it was essentially a calmly intoned reprise of the views he has expressed throughout the campaign.
While that may not fly with a foreign policy establishment that has teetered on the verge of panic over some of Mr Trump's more controversial proposals, this "America first" rhetoric has been at the heart of the message that has shot him to the top of the Republican heap.
Who are his advisers?
Mr Trump once said he was his own best foreign policy adviser, but, in recent months, has expanded his backroom team. Some of his appointments have proved controversial.
The team is led by Republican Senator Republican Senator Jeff Sessions of Alabama, a former federal prosecutor.
Another member, retired Gen Joseph Schmitz, resigned from the military in 2005 amid accusations of misconduct. However, Mr Schmitz was never charged with wrongdoing.
Another adviser, Walid Phares, was criticised when he was named as part of Mitt Romney's foreign policy team in 2011.
Muslim advocacy groups took issue with Mr Phares's close ties to right-wing Christian militia groups during the Lebanese civil war.
What do others think of Mr Trump's ideas?
"There was a lot in the talk that I would absolutely agree with," Jim Gilmore, a former 2016 Republican candidate, said. "On the other hand, there is a lot in this speech that contradicts that, that talks about pulling back, confronting if you will our allies much more."
White House spokesman Josh Earnest said: "I think when it comes to this president's foreign policy, there is no denying that the United States is safer and stronger than we were when President Obama took office back in January of 2009."
Mr Earnest also said other alliances had been strengthened, and that the new pivot to Asia had benefits the US economically and strategically.