Mr. Zhu said that China would also raise the allowed foreign investment in insurance companies, currently 50 percent for most companies, to 51 percent in three years and 100 percent in five years. China also plans to eliminate its current limit of 25 percent foreign ownership in banks, Mr. Zhu said, but he did not say when it might happen.

While the moves were announced several hours after Mr. Trump and his advisers flew to Vietnam, Mr. Zhu said that the initiatives were the result of decisions made during the Communist Party’s congress last month. Trump administration officials shied away from making commitments while in Beijing over market access, the sort of horse-trading that marked previous presidential visits. They have also been distracted by domestic issues and other trade issues.

Some international banking acumen may be welcome in China. The country’s state-controlled banking system has lent heavily to state-owned companies and affiliates of local governments, leading to vast piles of debt accumulated in a short amount of time. Meanwhile, some smaller businesses continue to complain about lack of access to money. Increased competition could spur state-owned banks to improve their lending decisions.

“Speaking over all, it is a good thing,” said Liu Dongliang, an analyst at China Merchants Bank. “There will be more different kinds of capital involved, and their management ideas and risk control ideas may arouse some reaction.”

American financial institutions cautiously welcomed the Chinese move. Citibank said that its existing operations in China were already growing, with more than $1 billion a year in China-related revenue, and that it wanted to study the details of the new regulations when they were released.

China promised when it joined the World Trade Organization in 2001 that it would rapidly open up its financial markets to foreign competition. Foreign commercial banks were then disappointed when Chinese regulators set high capital requirements for each foreign bank branch, limiting their ability to expand.

But the rise of online banking has reduced the need for bank branches, and so has the rise of electronic payments. Over the past couple of years, Citibank has been gradually closing some of its retail branches in China, as it has done in the United States. According to the bank, 95 percent of its retail banking transactions now take place outside bank branches.