White House trade advisor Peter Navarro told CNBC on Thursday the Trump administration is looking to make progress in "phase two" trade talks with China on U.S. demands that fell short in phase one.

The U.S. wants to work on getting China to stop subsidizing its state-owned enterprises, Navarro said on "Squawk Box," a day after the U.S. and China signed their phase one deal.

Navarro said China needs to stop "cyber intrusions."

"It's just insane that Chinese government officials continue to hack into American businesses and steal trade secrets," he added. "It's very destructive to our businesses."

Navarro said China also needs to curb the flow of illicit fentanyl.

President Donald Trump has widely criticized Beijing for not doing enough to prevent the highly addictive synthetic opioid from coming into the United States. Beijing denies that most of the illicit fentanyl entering the U.S. originates from China.

"The seventh deadly sin, of course is the fentanyl that kills over 50,000 Americans a year," Navarro said.

As for the initial trade deal signed on Wednesday, China agreed to end what the U.S. considers the practice of forcing or pressuring foreign companies to transfer their technologies to Chinese companies and to tighten intellectual property protections. China also agreed to purchase an additional $200 billion in U.S. goods over the next two years.

"We brought the Chinese to the bargaining table and we got them to sign a deal that's good for America," Navarro added.

The U.S., on its end, gave China some tariff relief. The phase one agreement, reached in December, canceled planned U.S. tariffs on Chinese-made smartphones, toys and laptop computers. It also cut in half to 7.5% the rate levied on about $120 billion worth of other China imports.

However, the U.S. is leaving in place 25% tariffs on a $250 billion array of Chinese industrial goods and components used by U.S. manufacturers.

Trump said at Wednesday's signing ceremony at the White House, "I will agree to take those tariffs off if we are able to do 'phase two.' In other words, we're negotiating with the tariffs."