WASHINGTON — President Trump on Friday ruled out rolling back all the tariffs he has imposed on China and indicated that he has not yet decided which levies, if any, he might eliminate as part of an initial trade agreement.

The comments came amid conflicting signals this week from the White House and China over the fate of Mr. Trump’s tariffs. The United States has already imposed levies on $360 billion worth of Chinese goods and another round is scheduled for December. China has been pushing to have some portion of tariffs rolled back as part of a “Phase 1” trade agreement and on Thursday, government officials confirmed that the Trump administration would eliminate some tariffs if a deal was reached.

What portion of the tariffs will be canceled and when remained a source of debate within the administration and on Friday, Mr. Trump signaled he was unwilling to do away with them entirely.

“They’d like to have a roll back — I have not agreed to anything,” Mr. Trump told reporters before departing the White House.

”China would like to get somewhat of a rollback, not a complete rollback, because they know I won’t do it,” he said.

Stocks, which started the day lower, dipped more after the president’s comments. But shortly after 11 a.m. the S&P 500 was down a scant 0.1 percent. It was the latest in a series of muted sessions, in which small gains have nonetheless pushed the market to new record highs.

Analysts have expected that America’s tariffs could be phased out over time as China meets certain benchmarks and demonstrates that it is keeping its commitments to respect American intellectual property, open its markets to foreign firms and purchase billions of dollars of agricultural product from the United States.

The Chinese government indicated Thursday that both sides had committed to removing some tariffs as part of any deal. But Mr. Trump’s advisers are once again at odds over whether to remove the tariffs, which have been used to punish China for years of unfair trade practices but are beginning to take a toll on the American economy.

Mr. Trump’s more moderate advisers have warned him that the tariffs, which are inflicting pain on farmers and manufacturers, could hurt him politically as he heads into re-election. But his more hawkish advisers are pressing him to keep the levies in place until China agrees to make more significant changes to its economic practices.

Larry Kudlow, the chairman of the White House’s National Economic Council, told Bloomberg News on Thursday that “if there’s a Phase 1 trade deal, there are going to be tariff agreements and concessions.”

Later in the day, Peter Navarro, one of Mr. Trump’s trade advisers, said that it was too soon to say that tariffs would be rolled back and that the president had not made a decision.

White House officials had been targeting the Asia-Pacific Economic Cooperation summit in Chile later this month as a venue where Mr. Trump and his counterpart, Xi Jinping, could meet and close the deal. That plan was derailed last week when the Chilean government canceled the summit amid political unrest in the country.

Mr. Trump said that if a signing ceremony with Mr. Xi takes place, he would like it to be held in the United States. He suggested that Iowa or somewhere in “farm country” would be preferable.

“It will be in our country,” Mr. Trump said.

Still, the president said that the agreement was not a sure thing and insisted that China wanted to make a deal more than he did.

“I never like to talk about things before we have them,” Mr. Trump said.

— Matt Phillips contributed reporting from New York.