Foreign-ministry officials told lawmakers on Tuesday that far from criticizing Australia’s refusal to accept migrants, several countries at a May meeting in Thailand on the region’s asylum-seeker crisis had sought its help on deterrence measures.

“If anything, there was positive interest in what we were doing and how we were doing it,” said Andrew Goledzinowski, appointed last year as Australia’s envoy for people-smuggling issues. “There was intention on the part of some delegations to continue that dialogue bilaterally.”

Australia’s Prime Minister Tony Abbott has been strongly criticized by refugee advocates and humanitarian groups for not matching offers from the U.S. and the Philippines to help resettle Burmese Rohingya and Bangladeshi migrants fleeing persecution or poverty. Instead he has offered a blunt “nope, nope, nope.”

Mr. Abbott last month said offering asylum seekers temporary haven in Australia could inflame rather than ease Southeast Asia’s human-trafficking problem, by encouraging more people to risk their lives by attempting the crossing.

The conservative government led by Mr. Abbott has enacted one of the toughest anti-asylum border operations in the world, with a military-led blockade of approaching boats and an uncompromising public campaign in asylum-source countries. Billboards in countries including Indonesia and Pakistan declare in block letters, “No way. You will not make Australia home.”

Since hundreds of would-be migrants drowned in the Mediterranean trying to get from Africa to Europe in April, Mr. Abbott has also held up his country’s immigration approach—criticized by the United Nations as a rejection of Australia’s refugee obligations—as a model for European governments vexed by their own burgeoning migrant problem.

Mr. Goledzinowski told a committee of lawmakers with foreign-affairs oversight that around 3,000 migrants were still thought to be at sea in Southeast Asia, although there is considerable uncertainty given the opaqueness of the people-trafficking trade.

He said none of Australia’s neighbors—a group in which he included Thailand, Malaysia and Indonesia—had asked the country to accept migrants on humanitarian grounds. By contrast, Australia’s communications strategies to deter asylum seekers had drawn considerable interest, he said.

“My expectation is that one and possibly more countries will come to us in the next weeks and months looking for specific assistance and advice on how to implement strategic communications strategies to try and counter the message of people traffickers and smugglers,” Mr. Goledzinowski said.

Source: The Wall Street Journal