Donald Trump launched a new war on terror last night and vowed to eliminate Islamic State 'from the face of the earth'.

But his bold declaration to 'eradicate completely' radical Islamic terrorism was at odds with his inauguration speech's 'America First' inward-looking agenda.

And it was not clear how Mr Trump and his advisors plan to succeed without jeopardising international relations and running up huge costs on military operations.

President Donald Trump delivers his inaugural address after being sworn in as the 45th president of the United States

While he has previously promised a more effective military campaign than that of Barack Obama, many of the actions he might take to accelerate progress in Iraq and Syria come with potentially dangerous side effects.

Those include the deterioration of already strained ties with NATO ally Turkey, an increase in American or civilian casualties and reinvigorated militant recruitment.

It is extraordinary, given the tentacles of the terror group extend across Syria, Iraq, Turkey, Tunisia and Libya, as well as parts of France, Belgium, Italy – and Britain.

Sceptics were also quick to point out that several past presidents, most notably George W. Bush, had failed to keep similar promises to beat terrorism. Yet in his speech, Mr Trump threw down the gauntlet to Islamic State and its supporters around the world.

He said: 'We will reinforce old alliances and form new ones – and unite the civilised world against radical Islamic terrorism, which we will eradicate completely from the face of the Earth.

'We will be protected by the great men and women of our military and law enforcement and, most importantly, we are protected by God.'

Donald Trump launched a new war on terror last night and vowed to eliminate Islamic State 'from the face of the earth'

Donald Trump is sworn in as the 45th president of the United States by Chief Justice John Roberts as Melania Trump looks on during the 58th Presidential Inauguration at the U.S. Capitol in Washington, Friday, Jan. 20, 2017

He has said that on taking office, he will tell his top generals they have 30 days to present him with a plan for defeating IS.

Later, his administration expanded on the plans to defeat terrorism.

A statement on the White House website said: 'Defeating ISIS and other radical Islamic terror groups will be our highest priority. To defeat and destroy these groups, we will pursue aggressive joint and coalition military operations when necessary.

In addition, the Trump administration will work with international partners to cut off funding for terrorist groups, to expand intelligence sharing, and to engage in cyberwarfare to disrupt and disable propaganda and recruiting.

'Next, we will rebuild the American military. Our Navy has shrunk from more than 500 ships in 1991 to 275 in 2016. Our Air Force is roughly one third smaller than in 1991.

'President Trump is committed to reversing this trend, because he knows that our military dominance must be unquestioned.

Donald Trump is sworn in as the 45th president of the United States by Chief Justice John Roberts as Melania Trump looks on

U.S. President Donald Trump (L) takes the oath of office from U.S. Supreme Court Chief Justice John Roberts (R) with his wife Melania, and children

'Finally, in pursuing a foreign policy based on American interests, we will embrace diplomacy. The world must know that we do not go abroad in search of enemies, that we are always happy when old enemies become friends, and when old friends become allies.

The world will be more peaceful and more prosperous with a stronger and more respected America.'

He also pledged to 'reinforce old alliances' in a sign that Britain's special relationship with the US could be boosted under his leadership. In response, Theresa May said she was certain Mr Trump intends to advance links between Britain and the US. She said: 'I congratulate President Trump on taking office today.

'From our conversations to date, I know we are both committed to advancing the special relationship between our two countries and working together for the prosperity and security of people on both sides of the Atlantic.'

Foreign Secretary Boris Johnson voiced his hopes for the continuation of the special relationship as he congratulated Mr Trump.

He tweeted: 'Look forward to continuing strong UK-US bond.'