Australia angered China last month after Turnbull's government stopped the A$10 billion ($7.57 billion) sale of the country's biggest energy grid to Chinese bidders after they failed to overcome security concerns.
After a meeting on the sidelines of a G20 summit in the eastern Chinese city of Hangzhou, Xi said China "hopes the Australian side continues to dedicate itself to providing foreign investors a fair, transparent and predictable policy environment".
"This also accords with Australia's own interests," China's Foreign Ministry quoted Xi as telling Turnbull.
The decision has caused a rift between Australia and its biggest trading partner. China has accused Australia of bowing to protectionist sentiment in blocking the bid for Ausgrid, as well as an earlier one by a China-led consortium to buy cattle company Kidman & Co.
Speaking to reporters later, Turnbull said China understood as well if not better than anyone else that it was Australia's sovereign right to determine who invests there and the terms in which they invest.
"China has more freedom to invest in Australia, indeed all foreigners have more freedom to invest in Australia, than in almost any other country. We have a very open foreign investment policy," Turnbull said.
"So we mostly say yes, we almost invariably say yes, but from time to time we say no and we make no bones about that and China respects that."
He added that the Ausgrid case was not specifically mentioned in the meeting.
Australia, a staunch U.S. ally, has also drawn criticism from China for running surveillance flights over disputed islands in the South China Sea, and supporting U.S. freedom of navigation exercises there.
Xi said China and Australia should respect each other's "choices in their development paths and each other's core interests and major interests", the foreign ministry added.
Turnbull said he discussed the South China Sea with Xi, and the importance of complying with international law.
"We're a good friend of China and good friends are very honest with each other," he added.
"We are consistent and our position is very clear that we expect and encourage all parties to comply with the rule of law, to show restraint and not act in a way that would exacerbate or create tensions." - Reuters
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