President Barack Obama urged Beijing to take "concrete steps" to ease tensions over cyber hacking and its wide-ranging maritime claims, as the United States and China ended three days of candid talks.

American officials have voiced deep concerns about both issues at the annual strategic and economic dialogue aimed at setting guidelines to steer future ties between the world's two leading economies.

Dual nationals who help terrorists could automatically lose their Australian citizenship even if they have never stepped foot out of the country under new laws introduced to parliament on Wednesday.

Immigration Minister Peter Dutton introduced legislation to amend the Citizenship Act as fears grow about the number of Australians fighting with jihadist groups and concern about the threat at home from radicalised individuals.

The mother-in-law of one of a Lebanese man and Australia's most notorious Islamic State fighters has pleaded for the government to help her "desperate" daughter and five grandchildren flee the Middle East, saying she made "the mistake of a lifetime.”

Karen Nettleton's emotional appeal for help came after reports that her son-in-law Khaled Sharrouf and his friend Mohamed Elomar were killed in fighting in the Iraqi city of Mosul in the past week, although officials Wednesday suggested they may have died in Syria .

Australia said Tuesday it will introduce new laws this week to strip dual nationals linked to terrorism of their citizenship, but backed away from putting the power in the hands of a single minister.

The legislation will see the Citizenship Act -- which currently stipulates a person ceases to be a national if they serve in the armed forces of a country at war with Australia -- expanded to include people who "fight against us in a terrorist group".

Reports that a Lebanese-Australian terrorist, notorious for holding up the severed heads of Syrian victims, has been killed fighting in Iraq have raised the potential for his young family to be repatriated from the Middle East, Australia's foreign minister said on Tuesday.

Australian intelligence agencies were attempting to verify the recent deaths of Australians Khaled Sharrouf and Mohamed Elomar in the Islamic State-held city of Mosul in Iraq, Foreign Minister Julie Bishop said. Both men were seen in photographs posted on social media holding heads of Syrians.

Moscow will extend its embargo on European Union agricultural products but is unlikely to go further if the EU extends sanctions as expected, economy minister Alexei Ulyukayev said Thursday.

"We'll just keep the status quo: the embargo on produce introduced in response to the sanctions regime -- of course, it's a symmetrical measure," Ulyukayev told RIA Novosti state news agency.

An arrest warrant was issued Thursday for an Australian-trained doctor who appeared in an Islamic State propaganda video which urges other medical professionals to join the jihadists, police said.

Tareq Kamleh was shown in the slick video, uploaded to YouTube in April, identifying himself as Abu Yusuf and explaining that he traveled to the city of Raqa in Syria to use his medical skills in the IS cause.

Australians support the country's involvement in the fight against the Islamic State group (IS) in Iraq, despite fears it raises the risk of terror acts against them, a poll revealed Tuesday.

The 2015 Lowy Institute Poll found that 69 percent of Australians were in favor of the current involvement in air strikes against the jihadists and providing support for Iraqi security forces.

Australian authorities work within the law to stop asylum-seeker boats, Prime Minister Tony Abbott insisted Tuesday after reports officials have made cash payments to members of people-smuggling rings for years.

The government has refused to deny reports that six Indonesian crew members were paid $US5,000 each to return an asylum-seeker vessel to Indonesia in late May, saying no comment will be made on operational issues.

Indonesia's vice president warned Monday that paying people-smugglers would amount to "bribery" after Australia was accused of handing out money to turn back a boatload of asylum-seekers.

Allegations that the captain and five crew of a boat, carrying migrants from Bangladesh, Myanmar and Sri Lanka, were each paid US$5,000 by an Australian immigration official to turn back to Indonesia were made to police on Rote island in the country's east last week.