Homeland Security Secretary John Kelly has said he hoped to have a wall along the southern US border with Mexico finished within two years, according to an interview with Fox News.
"The wall will be built where it's needed first, and then it will be filled in. That's the way I look at it," Mr Kelly said in the interview.
"I really hope to have it done within the next two years."
He added he thought funding from Congress for the massive project would come "relatively quickly."
Earlier US President Donald Trump said that the world is in trouble, the United States is being taken advantage of, and that he was having "tough phone calls" as he worked to address issues.
His comments, at a national prayer breakfast this morning, come after reports of an acrimonious telephone call he had with Australia's prime minister.
Mr Trump said: "The world is in trouble, but we're going to straighten it out, OK? That's what I do - I fix things.
"Believe me, when you hear about the tough phone calls I'm having - don't worry about it. Just don't worry about it.
"We're taken advantage of by every nation in the world virtually. It's not going to happen anymore," he said.
Mr Trump had earlier labelled a refugee swap deal with Australia "dumb" after a Washington Post report of a phone call with Australian Prime Minister Malcolm Turnbull threatened a rare rift in ties between the two staunch allies.
The Post reported that Mr Trump described the resettlement plan as "the worst deal ever" and accused Australia of trying to export the "next Boston bombers".
It said the call had been scheduled to last an hour but Mr Trump cut it short after 25 minutes when Mr Turnbull tried to turn to subjects such as Syria.
Mr Turnbull told reporters the call with Mr Trump at the weekend had been frank and candid but refused to give further details.
"I do stand up for Australia. My job is to defend Australian interests," Mr Turnbull said in Melbourne.
Mr Turnbull refused to confirm the Post report that Mr Trump, who had earlier spoken to world leaders including Russian President Vladimir Putin and Mexican President Enrique Peña Nieto, had angrily told him that the call was "the worst so far".
Political analysts said such acrimony was unprecedented, surpassing even the difficult relations between former US President Richard Nixon and then Australian Prime Minister Gough Whitlam, who pulled Australian troops out of the Vietnam War.
"Even that was always done in the language of foreign policy niceties," said Harry Phillips, a political analyst of 40 years experience at Edith Cowan and Curtin universities in Perth.
As reports of the conversation hit headlines on both sides of the world, Mr Trump tweeted shortly before midnight in Washington: "Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal."
Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!
— Donald J. Trump (@realDonaldTrump) February 2, 2017
That threw more confusion over the status of the controversial deal Australia agreed with former president Barack Obama late last year for the United States to resettle up to 1,250 asylum seekers held in offshore processing camps on Pacific islands in Papua New Guinea and Nauru.
In return, Australia would resettle refugees from El Salvador, Guatemala and Honduras.
The swap deal is at odds with Mr Trump's executive order last week that suspended the US refugee programme and restricted entry to the United States for travellers from seven Muslim-majority countries, including Iran, Iraq, and Syria.
Many of those being held in the Australian detention centres, which have drawn harsh criticism from the United Nations and rights groups, have fled violence in countries such as Afghanistan, Iraq and Iran.
White House spokesman Sean Spicer and the US Embassy in Australia have both said Mr Trump would honour the deal.
In several media appearances after Mr Trump's tweet, Mr Turnbull reiterated that he believed the deal stood.
"He is saying that this is not a deal he would have made, but the question is will he honour that commitment? He has already given it," Mr Turnbull said.
"I make Australia's case frankly, powerfully, forthrightly and hopefully persuasively when I deal with other leaders."
The apparent breakdown between Washington and Canberra that has developed over the resettlement deal could have serious repercussions.
Australia and the United States are among the five nations that make up the Five Eyes group, the world's leading intelligence-sharing network.
The United States also plans to send extra military aircraft to Australia's tropical north this year as part of a US Marines deployment that will bolster its military presence close to the disputed South China Sea.
Australia is also one of ten US allies purchasing Lockheed Martin's F-35 fighter jet programme.
The Post quoted unidentified senior US officials briefed on the conversation between Mr Trump and Mr Turnbull.
It also quoted the official read-out from the call, which emphasised "the enduring strength and closeness of the US-Australia relationship that is critical for peace, stability, and prosperity in the Asia-Pacific region and globally".
It also said Mr Trump had boasted to Mr Turnbull about the size of his election victory.
