While the U.S. is expected to continue to raise rates aggressively, the Bank of Japan has now held short-term rates in negative territory for more than six years. Mr. Kuroda said that despite Japan having “somewhat miraculously” achieved core consumer inflation of 2.4%, it wouldn’t last. He said inflation could go higher this year but he expected it to go back down to 1.5% in 2023.

“So we have no choice other than continued monetary easing until wages and prices rise in a stable and sustainable manner,” Mr. Kuroda said.

The Jackson Hole comments from Mr. Powell and Mr. Kuroda make clear the sharp difference in monetary-policy direction between the central banks of the U.S. and Japan. Traders, analysts and economists said that is the major explanation for the rising value of the dollar against the yen.

On Friday afternoon in Tokyo, the yen was trading at 140.12 to the dollar, its lowest level since August 1998. That compares to 115 yen per dollar at the end of 2021, representing a fall of around 18% since the start of the year.

The difference in interest-rate expectations between the two countries is the key driver of the move, said Bart Wakabayashi, the co-manager of State Street Bank and Trust Co.’s Tokyo branch. He said it wasn’t just the direction of interest rates that was important but also a widespread belief the two central banks would hold steady until they had met their inflation targets—however long that takes.

“The BOJ and the Fed have the respect of the market, they have credibility,” he said. “There were some dissenters regarding the Fed’s direction, but after Jackson Hole everyone is on board now.”

The Fed and the Bank of Japan both aim for inflation of around 2%. U.S. consumer price inflation was 8.5% in July, and core inflation—which excludes food and energy prices—was 5.9%.

Japan’s core inflation, which measures all goods except fresh food, hit 2.4% in the same month, but the central bank doesn’t think it will last. The median forecast of the Bank of Japan’s policy board is for 1.4% core inflation in the year ending March 2024. Japan’s own inflation measure that leaves out food and energy prices was 1.2% in July.

The Fed increased rates by three-quarters of a percentage point in June and July, and the markets still expect aggressive hikes. The benchmark federal-funds rate is now in a range between 2.25% and 2.5%. The Bank of Japan, in contrast, has kept an important short-term rate at minus 0.1% since January 2016.

In theory, a weaker yen should fuel inflation in Japan, by making local goods cheaper for foreign buyers and foreign goods more expensive. But there has been little evidence of that happening, said Hiroshi Shiraishi, a senior Japan economist at BNP Paribas.

“Inflation in Japan is being driven primarily by higher imported commodity prices,” he said. “We haven’t seen much inflation besides that.”

The slow pace of wage growth in Japan is one reason. Japanese workers tend to put more focus on the stability of their jobs rather than the size of their pay packets, meaning rising energy or food prices don’t quickly translate into higher salaries, said Mr. Shiraishi. Bank of Japan policy board members said in late August that they weren’t ready to tighten monetary policy because wage growth hasn’t caught up with inflation.

Mr. Kuroda says the central bank doesn’t target foreign-exchange rates and it isn’t rational to use rate increases as a tool to fix the yen’s weakness.

“If we want to stop the yen from weakening only by adjusting interest rates, we would need huge rate increases, and it would cause significant damage to the economy,” he said at a news conference in late July.

Osamu Takashima, a currency strategist at Citi, agreed that it would be a “big risk” for the Bank of Japan to raise interest rates to defend the currency. “It’s a smart judgment by the central bank to not touch it,” he said.

Mitsubishi UFJ Morgan Stanley Securities

strategist Naomi Muguruma said a surprise rate increase might lead traders temporarily to unwind positions betting on a fall of the yen, but she said the effects probably wouldn’t last for long and markets would demand more rate increases.

—Nick Timiraos contributed to this article.

Write to Matthew Thomas at matthew.thomas@wsj.com and Megumi Fujikawa at megumi.fujikawa@wsj.com