The world has embraced the Barack Obama era, but leaders warn that the new US president will have to deal with many difficulties ahead.

Taoiseach Brian Cowen welcomed a 'a day of joy and celebration in Washington, across the United States and across the world.'

Praising what he called a new beginning for America, Mr Cowen offered 'congratulations, best wishes and support on behalf of the people of Ireland.'

'His inaugural address offered inspiration and hope to us all.'

Millions followed the inauguration around the world and underscoring the huge show of faith, French President Nicolas Sarkozy said: 'We are eager for him to get to work so that with him we can change the world.'

British Prime Minister Gordon Brown also hailed Barack Obama's inauguration as a 'new chapter in both American history and the world's history.'

Barack Obama was a 'man of great vision,' Brown said. 'He's not only the first black American president but he sets out with the determination to solve the world's problems.'

The welcome for the Obama administration extended to the Far East as Japanese Prime Minister Taro Aso vowed to work with the new president to boost 'peace and prosperity in the Asia-Pacific region and the world.'

Obama parties were held in capitals from Dublin to Sydney and thousands celebrated in the Kenyan village where his father was born.

In Moneygall, Co Offaly, distant relatives of Barack Obama gathered to watch the inauguration of a new president, while in Co Louth the occasion was marked by the malting of a new whiskey to celebrate the Irish Ancestral links to the Whitehouse.

High expectations

But some leaders sought to douse the world's high expectations.

German Chancellor Angela Merkel wished Obama 'the best of luck', but gave the latest in a series of warnings to the new US president - this time about sending troops to Afghanistan and dealing with Iran.

She said Obama would not sway Germany to add further to its committed 4,500 force in Afghanistan.

'We took our decisions based on our capabilities, our skills - not on who is president.'

President Obama inherits an economy in crisis, wars in Afghanistan and Iraq and a conflict in the Middle East where the United States has a key role, even though its world standing is considered lower than at any time for decades.

Pope Benedict XVI sent a message to Mr Obama, calling on him 'to promote understanding, co-operation and peace' among nations.

In Gaza, where a fragile ceasefire holds after a three-week Israeli offensive in which more than 1,300 Palestinians were killed, residents were sceptical of the influence a US President would have on them.

'Obama won't bring my husband back to life', widowed mother of six Leila Khalil said.

On the other side of the Middle East divide, Israeli opposition leader Benjamin Netanyahu said he had the impression that 'Barack Obama understood our distress very well, as well as the cruelty of the enemies we face.'

Russian Prime Minister Vladimir Putin has also sought counter the optimism.

'I am deeply convinced that the biggest disappointments are born out of big expectations,' he said during a trip to Berlin.

China said Obama would have to work on stronger military ties between the two countries. Ministry of Defence spokesman Colonel Hu Changming said there were 'difficulties' in military relations with the world superpower.

International polls have, however, shown huge public support for the Democratic President.