Maximum pressure must be exerted on North Korea, Turnbull said.
Early today, May visited a United States naval base on the outskirts of Tokyo with Japanese Defence Minister Itsunori Onodera before attending a business forum.
"Working with China is important and needs to be pursued, but I think to some extent the Trump administration has pursued it more as an outsourcing option", said Mr Hill, a former assistant secretary of state for East Asian and Pacific affairs.
But Japanese officials on Tuesday shot down the UK's hopes for a quick trade agreement, saying said they were in no rush to enter negotiations with Britain, especially since it is now negotiating a free trade agreement with the EU.
May will also discuss defence cooperation, describing Japan as "our closest security partner in Asia".
However, Labour MP Alison McGovern accused ministers of focusing on "imaginary trade deals" rather than shoring up existing agreements as it emerged that Britain could come out of 13 bilateral agreements between Japan and the EU.
Early today, May visited a naval base on the outskirts of Tokyo with Defence Minister Itsunori Onodera before attending a business forum and the security meeting.
The auto industry remains nervous about Britain leaving the European Union, Aston Martin CEO Andy Palmer told reporters in Tokyo, warning that executives are considering holding back investment until there's more certainty on the direction of Brexit.
Exporters gained ground after the dollar last traded at 109.85 yen, having recovered from Tuesday's low of 108.265 yen, which was the greenback's lowest level since mid-April.
Gold prices fell from a more than nine-month high and the dollar pulled away from its 4-1/2 month lows against the yen after North Korea said the launch of an intermediate-range ballistic missile over Japan was to counter US and South Korean military drills.
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"I believe that China should be using its leverage with North Korea to ensure that [it] stops these illegal tests", the Prime Minister told Sky News in Kyoto on Wednesday.
Japanese businesses employ about 140,000 people in the United Kingdom, including a number of major banks, as well as carmakers such as Nissan, Toyota and Honda.
However Liberal Democrat Chief Whip Alistair Carmichael criticised the announcement, saying that Mrs May went to Japan seeking a new trade deal but instead had to admit the "biggest priority will be completing the one the European Union is already negotiating".
British Prime Minister Theresa May has visited a Japanese warship ahead of a summit with her Japanese counterpart.