Britain will remain a "major player in the world" despite the rise of new economic powers, David Cameron has said in a set-piece foreign policy speech.
The UK remained a "great economic power" and there was no reason its military power would diminish, he said.
But Britain must "sort out" its economy if it wants to "carry weight in the world", the prime minister said.
There have been questions about whether defence cuts will mean the UK has to scale back future military operations.
BBC political editor Nick Robinson said predictions of the decline of the City of London and of the global dominance of the big Western powers, cuts to Britain's military and questions about Mr Cameron's stance on projecting British power abroad had fuelled the arguments that Britain was embarked on an inevitable path of decline.
But in his first annual speech to the Lord Mayor's Banquet at London's Guildhall, Mr Cameron rejected any argument Britain is "in decline" internationally.
He rejected the argument that the rise of new powers spelled the end for Britain's influence in the world, saying: "Britain remains a great economic power. Show me a City in the world with stronger credentials than the City of London."
But he said the quicker the UK gets its economy in order, the more substantial and credible its international impact will be: "Economic strength will restore our respect in the world and our national self confidence."
He stressed the need to be "hard headed" in its foreign policy and also put "commercial interest" at its heart.
Mr Cameron said he wanted Britain to be "first in the world" as a place to do business, that he would continue to build on the UK's "crucial" relationship with the US but also pledged to link up Britain's economy with the "fastest growing parts of the world" - such as India, Turkey, China, Brazil and Russia.
He also defended the strategic defence review, arguing "tough choices" had been necessary because of the deficit but Britain would be "one of the few countries able to deploy a full equipped brigade sized force anywhere in the world".
And he said the government would learn lessons from Iraq - where "there was no plan for winning the peace" - and Afghanistan, where "we failed to think through the implications of the decision to deploy into Helmand Province".
The prime minister also defended his pledge to protect international aid spending, saying he would meet the target to spend 0.7% of national income on aid by 2013 - arguing it saved lives, prevented conflict and was the "most visible example of Britain's global reach" for millions of people.
Mr Cameron said some were "quick to prophesy dark times ahead" for Britain: "Our foreign policy runs counter to that pessimism. We have the resources, commercial, military and cultural, to remain a major player in the world."
On Sunday Robert Kagan, former foreign affairs adviser to Senator John McCain, told ABC News on Sunday: "Britain has taken itself out as a major player in the international system, at least for a while, with the kind of cuts that they've made in their national security budget."
And US Secretary of State Hillary Clinton, speaking before the UK's wide-ranging defence review was published, was asked on the BBC whether the scale of defence spending cuts in countries like the UK worried Washington.
She said: "It does, and the reason it does is because I think we do have to have an alliance where there is a commitment to the common defence."
In the Commons on Monday, Labour deputy leader Harriet Harman said the weekend G20 summit of world leaders in Seoul had been a "missed opportunity".
She added: "Britain needed to send a statesman to this summit but all we sent was a spectator."
But, in a statement updating MPs on the meeting, Mr Cameron said "important progress" had been made on dealing with global economic tensions.
He told MPs: "If Labour had been there at this G20 they would have been completely isolated over the issue of the deficit.
"Everyone else in the room was signing a communique about how we have to take early action on deficits. That is the consensus. They are completely outside the consensus."
The summit failed to deliver the 4% limit on national trade deficits and surpluses proposed by US President Barack Obama, which was blocked by exporting countries China and Germany. But world leaders agreed to develop new guidelines to prevent "currency wars".