Turnbull congratulates Trump

Prime Minister Malcolm Turnbull has congratulated Donald Trump after he officially became the 45th President of the United States, saying he anticipated a "great future" for the two nations.

"Congratulations President Trump," Mr Turnbull tweeted to Mr Trump's new @POTUS twitter handle.

"We are steadfast allies & trusted friends with a great future ahead of us. We wish you every success."

It came after Mr Trump used his first speech as US president to sound a warning to Australia and other countries around the world that a new era had begun with his arrival in the White House.

Trump didn't specifically refer to the proposed Trans-Pacific Partnership, but the pact championed by Obama between the US, Australia, New Zealand, Japan and eight other Pacific countries is likely to be scrapped within days.

Opposition trade spokesman Jason Clare said the Australian government needed to consider alternative trade agreements, now that the Trans-Pacific Partnership was dead.

"Throughout the week Malcolm Turnbull has said that he can convince Donald Trump to change his mind, well now it's clear that he can't," Mr Clare said.

A spokesman for the prime minister said the government remained committed to the TPP and its position on it had not changed.

Mr Turnbull was not present at the inauguration ceremony in Washington DC, which was attended by Australia's ambassador to the US Joe Hockey.