Larry Kudlow said the recent call for trade with China "has gone very well"

White House economic adviser Larry Kudlow said the recent trade talks with China "went very well".

"The phone call of the day before yesterday evening with the Secretary of State Mnuchin, Lighthizer and Deputy Prime Minister Liu, went very well, it is important", said Kudlow at Squawk on the Street, CNBC. "The telephone lines were opened during this period and negotiations are continuing."

Liu He, China's chief trade negotiator, US Trade Representative Robert Lighthizer and Treasury Secretary Steven Mnuchin held a phone call on Wednesday and agreed to meet in early October for a new round of talks.

"The level of deputies [meeting] will continue in Washington later this month and from that the meetings at the deputy minister level will come on the agenda and will outline the principles with meeting early October, "Kudlow said. I think it is extremely important. "

USTR spokesperson said earlier this week that the two countries "agreed to hold ministerial meetings in Washington in the coming weeks" and that deputy minister level meetings will take place in mid-September "to prepare the ground for significant progress".

Many market participants and Chinese insiders believe that these new negotiations could lead to substantial results. Both countries have been engaged in a trade war for 18 months now. The meetings will follow the latest round of tariffs on billions of dollars worth of goods from each country that took effect on Sunday.