"They made headway on specific issues and the two sides are close to finalizing some sections of the agreement," USTR said. "Discussions will go on continuously at the deputy level, and the principals will have another call in the near future."

The agency issued a statement outlining the status of discussions following a conversation that U.S. Trade Representative Robert Lighthizer and Treasury Secretary Steven Mnuchin had with Chinese Vice Premier Liu He.

The U.S. and China have made progress in trade discussions and have come close to finalizing parts of a phase one deal, the Office of the U.S. Trade Representative said Friday.

Liu He, China's vice premier, left, and Robert Lighthizer, U.S. trade representative, wave to members of the media before a meeting at the Office of the U.S. Trade Representative in Washington, D.C., U.S., on Friday, Oct. 11, 2019.

The world's two largest economies have pushed for a trade agreement as they try to end a potentially devastating series of tariffs on hundreds of billions of dollars worth of each other's goods. President Donald Trump aims to resolve longstanding concerns about Chinese theft of U.S. intellectual property and forced technology transfers, and secure more Chinese purchases of U.S. agricultural goods.

Asked about China on Friday, Trump said, "We're doing very well."

"We're moving along nicely. We're dealing with them right now," he told reporters before leaving Washington for South Carolina. "And a lot of good things are happening with China. They want to make a deal very badly."

Earlier this month, Trump announced the sides reached a "very substantial phase one deal" to be finalized over three weeks. He said the agreement would address issues such as intellectual property and financial services and include a pledge for China to buy $40 billion to $50 billion in American agricultural products.

Trump called it a "tremendous deal for the farmers" as he tries to contain damage from Beijing's retaliatory tariffs on U.S. crops.

The Trump administration also ditched a planned tariff hike on $250 billion in Chinese goods that was set to take effect Oct. 15. Reports suggested Beijing also wanted the U.S. to abandon another tariff increase set for December.

Despite Trump's public optimism about an agreement, doubts lingered in recent days about the countries' ability to sign a deal. Chinese state media had cautioned about becoming too hopeful.

On Wednesday, Sen. Marco Rubio, R-Fla., told CNBC that "it's been very difficult to get the Chinese to admit the they agreed to what has been reported they agreed to."