By: Australian Associated Press in DailyMail.com

Australia's monopoly on a unique US work visa appears set to be broken with President Donald Trump reportedly ceding to a lobbying effort by Ireland.

The E3 is a two-year visa allowing Australian professionals and their spouses to work in the US with no limit to the number of additional two-year extensions.

The US does not offer the E3 to any other nation, but that could soon change after it was on Irish Prime Minister Leo Varadkar's agenda when he met with Trump at the White House on Thursday, held a breakfast with Vice President Mike Pence and participated in St Patrick's Day events with members of US Congress.

Australian Ambassador Joe Hockey successfully led a lobbying effort late last year that thwarted Ireland's attempts but Trump and leaders in Congress appear to be backing Ireland's bid.

"This week in Washington it was made clear to us by all the leaders of both parties that they want to get the E3 Bill passed," Ireland's special US envoy John Deasy told the Irish Examiner.

Trump reportedly told Varadkar the bill should be filed again.

"I want to thank you and Congress for your support for a new E3 visa program, which would allow a limited number of Irish people to come here annually," Varadkar told Trump at the traditional bowl of shamrock event at the White House on Thursday.

It was just one senator, Arizona Republican and immigration hardliner Tom Cotton, who blocked the bill last year.

Trump and Pence reportedly spoke to Cotton earlier this week about supporting the Irish.

Democrat congressman Richard Neal and Republican Jim Sensenbrenner are expected to reintroduce the bill.

Australia was first rewarded with the E3 in 2005 following its support for the US during the Iraq War and the signing of the US-Australia free trade agreement.

Each year 10,500 E3 visas are made available to Australians but only about half are snapped up.

Ireland is seeking the leftovers.

In return, Ireland may ease restrictions for American citizens who want to retire to Ireland.