OSAKA, Japan — President Donald Trump and Chinese counterpart Xi Jinping agreed Saturday to resume high-level negotiations for a landmark new trade agreement, a development they hope will end a trade war that has roiled markets and raised prices worldwide.

The new talks are designed "to see if we can make a deal," Trump told reporters at the end of the G-20 summit in Japan.

Trump, who said he will hold off on new tariffs on China as talks progress "at least for the time being," also announced that China agreed to buy more agriculture products from the United States.

American farmers, a politically important group, have been hit particularly hard by the China trade war.

Neither Trump nor China disclosed any concessions they might be willing to make in negotiations that have stalled in the past.

Nor did they put a timeline or deadline on new negotiations.

Trump, who flew to Seoul after the G-20 summit to confer with South Korean President Moon Jae-in, tweeted early Sunday that "the quality of the transaction" with China "is far more important to me than speed" of any new agreement.

"I am in no hurry, but things look very good!" he said.

While in Seoul, Trump is scheduled to visit the Demilitarized Zone between North and South Korea, and may speak with North Korean leader Kim Jong Un.

Also announcing plans to continue trade talks, the Chinese state-run news service Xinhua reported that "the U.S. side said it will not add new tariffs on Chinese exports. The two countries' economic and trade negotiating teams will discuss specific issues."

'I did say it':Trump defends his exchange with Vladimir Putin over election meddling

The announcements came after Trump and Xi sat down to re-start talks for a new agreement that could end the trade war between the world's two largest economies.

"We're totally open to it ... I think this could be a very productive meeting," Trump told Xi as they began their meeting on the sidelines of the G-20 summit in this ancient Japanese port city.

Xi called the talks a potential turning point in the U.S.-Chinese relationship, and told Trump that their two countries "benefit from cooperation and lose in confrontation. Cooperation and dialogue are better than friction and confrontation."

Marianne Williamson:Republicans start donating to Marianne Williamson to keep her in future Democratic debates

Hours before his meeting with the Chinese leader, Trump and his aides expressed guarded optimism that the two nations – the largest economies in the world –could at least resume negotiations that broke off in May.

Trump had said he was prepared to put more tariffs on Chinese goods if the Xi meeting didn't go well. The Chinese said they were prepared to do much the same thing to American products.

Those threats are now in abeyance as both sides resume talks on a potential new agreement.

"As to whether or not we can make a deal, time will tell," Trump told reporters.

Trump at G-20:Trump's own brand of diplomacy is on display at G-20. How will it fare with Valdimir Putin, Xi Jinping?

Noting that he saw Xi at a G-20 event Friday, Trump said "the relationship itself is really good," and that he and the Chinese president "have a very good friendship, a very, very good friendship.”

For months, the two countries have taken turns hitting each other with tariffs, raising prices for producers and consumers and slowing growth worldwide.

Trump and Kim:Trump on possible Korean DMZ meeting with Kim Jong Un: 'We'll see'

According to a study by the Federal Reserve Bank of New York, tariffs set in 2018 "imposed an annual cost of $419 for the typical household."

The renewal of negotiations takes place more than a month after U.S. and Chinese negotiators broke off trade talks, each side accusing the other of seeking to change the details at the last minute.

In remarks at the top of his meeting with Trump, Xi traced the up-and-down nature of the U.S.-Chinese relationship that he said began when an American table tennis team visited China for matches in 1971.

"That marked the beginning of what we now know as ping-pong diplomacy," Trump said.

Trump cited more recent history, saying the U.S. and China were on the verge of a deal little more than a month ago, but then "something happened."

Debate winners and losers:The winners and losers from 2 nights of sparring at the Democratic debates in Miami

"It would be historic if we could do a trade deal," Trump said.

Throughout his presidential campaign and into his presidency, Trump has repeatedly accused China of taking advantage of, even "raping," the United States with its trade policies.

The United States wants China to change some of its trade policies, particularly its demands that companies give up technology and trade secrets if they are to do business in the Middle Kingdom.

Xi, meanwhile, is making demands of his own. For one thing, he wants Trump to end his administration's ban on the sales of U.S. parts to Huawei Technologies Co., the Chinese telecommunications giant.

Trump said he will decide what to do with Huawei toward "the end" of the negotiations, but suggested he would allow American companies to continue selling certain high-tech equipment to the Chinese company.

In the run-up to the meeting, Chinese officials also said they wanted Trump to postpone the prospect of more tariffs for at least six months as talks continue. The United States is also seeking relief from Chinese tariffs.

More:Donald Trump invites Kim Jong Un to meet him at Korea border

Trade wasn't the only item on the Trump-Xi agenda. There's also North Korea.

Xi pitched a plan to revive U.S. negotiations with North Korea over the fate of its nuclear weapons programs.

After the end of the G-20 summit Saturday, Trump traveled to Seoul for his meetings with South Korean President Moon Jae-in — and possibly Kim himself.

Hours before the Xi meeting, Trump tweeted out an invitation to Kim to meet him at the Demilitarized Zone during his visit to Seoul.