As diplomats on both sides go about restoring a bit of civility in the relationship, four senators - two Republican, two Democrat - have introduced a bipartisan motion to reaffirm all that is great between Canberra and Washington - committing to an enduring alliance and support for continued diplomatic, military and economic co-operation; and reaffirming the importance of mutual respect to preserve shared national interests in the "Indo-Asia Pacific and around the world".

Backed by Republicans Marco Rubio and Lamar Alexander and Democrats Ben Cardin and Edward Markey, the tabling of the Senate motion coincided with a make-up phone conversation between Foreign Affairs Minister Julie Bishop and newly confirmed US Secretary of State Rex Tillerson.

Explaining what Trump didn't seem to get in the exchange with Turnbull, which he cut short after telling the Australian leader that it was the "worst" of a series of phone calls he made in the weekend, an apologetic Cardin said: "The US-Australia alliance is an anchor for peace and stability in the Asia-Pacific region and worldwide.

"Australia is one of our closest friends, and for decades we have co-operated on a host of global issues such as terrorism, climate change, infectious diseases and counter-narcotics. Australian has fought together with the United States military in every significant conflict since World War I, been a leading partner in combating [Islamic State], and played a critical support role for our Marines in the region."

He continued: "Underpinning our alliance is a strong sense of shared common values, histories, and ideals among the people of Australia and the United States. That bond is rooted in a sacred vow of friendship and trust, where Australia has always been a faithful and reliable partner to the United States, and that should go both ways. I am proud to introduce this resolution to reaffirm this sentiment and recommit to an even stronger relationship moving forward."

Alexander felt much the same: "The people of the United States do not have better friends than the people of Australia. As one Australian told me when my family lived in Sydney 30 years ago, 'Well, we're mates all right. The English may be our ancestors, but you Americans are our cousins - first cousins.'

"Today, no two countries trust one another and co-operate in security arrangements more than American and Australia. We trade, we stand by each other in war, we visit one another and our students study in each other's universities. It is always appropriate for the US Senate to reaffirm the importance of that relationship."

Markey directed strong words at Trump: "Today, as President Trump disparages and disrespects our longstanding partners and allies, it is more vital than ever to strengthen our relationship with Australia."

A similar motion was introduced in the House.

Tillerson's call to Bishop was one in a series to soothe anxious foreign ministers after comments from Trump that left Japan and South Korea, along with Australia, wondering what had become of their long-standing alliances with the US.

Despite Trump's isolationist rhetoric, State Department spokesman Mark Toner said that Tillerson had pledged to work closely with the three foreign ministers to tackle threats from North Korea's nuclear ambitions and increased tensions in the East and South China seas.

"Secretary Tillerson reiterated the administration's intent to strengthen our military alliances, our economic partnerships and our diplomatic cooperation," Toner said.

Offering more balm, Toner said that Tillerson wanted early meetings with his counterparts, to whom he had expressed "his deep respect for their nations' contributions to regional security, global prosperity, democratic institutions, and the rule of law".