China needs to do more than just buy more U.S. goods before the two countries strike a permanent trade deal, U.S. Trade Representative Robert Lighthizer told the House Ways and Means Committee on Wednesday.

"If we can complete this effort — and again, I say' if' — and can reach a satisfactory solution to the all-important and outstanding issue of enforceability, as well as some other concerns, we might be able to have agreement that does turn the corner in our economic relationship," Lighthizer said.

"We can compete with anyone in the world, but we must have rule, enforced rules, that make sure market outcomes and not state capitalism and technology theft determine winners."

Lighthizer's testimony comes after President Donald Trump pushed back a key early March deadline for the U.S. and China to strike a trade deal. Trump cited "significant progress" for pushing back the deadline. The Chinese also agreed to buy up to $1.2 trillion in U.S. goods, CNBC learned through a source.

"Let me be clear," Lighthizer testified. "Much still needs to be done both before an agreement is reached and, more importantly, after it is reached, if one is reached."

"It has to be specific, measurable; it has to be enforceable at all levels of government."

Wall Street has worried about increasing trade tensions between China and the U.S. for most of last year as investors gauged the potential impact of tariffs on the global economy.

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