Traders said that has been helpful to Japanese investors looking for a home for their cash amid very low yields in Japan.
"As long as US rates are rising you've got this double-whammy effect of spare cash looking for yield and yield is there," said Luke Waddington, head of forex trade at Royal Bank of Scotland in Tokyo.
"That's why dollar/yen is totally supported, and people underestimate the fact that this is probably going to be a theme for quite a few months to come."
The Fed has raised its benchmark interest rate at 11 successive meetings since June 2004, taking it to 3.75 percent, and many economists expect it to raise rates twice more this year to 4.25 percent, and probably more next year.
Meanwhile, the base rate in Japan is near zero, while the European Central Bank (ECB) has kept its key rate at 2 percent for over two years.
The dollar was down a little on the day at 115.80 yen. It climbed as high as 115.97 yen before turning tail just short of 116 yen - a key psychological level where a blockade of option-related sell orders is seen.
The dollar had matched a 25-month high of 115.98 yen on Friday, according to electronic platform EBS.
Some traders said that despite the dollar's inability to break through 116 yen, the currency was well-bid in Tokyo trading and the market could push it beyond that level once the London session got underway.
At the same time, other market participants continued to show concern about the ballooning number of short yen positions, which last week hit their highest level since May 1999, according to IMM data.
Some analysts said the pile-up of yen shorts could prompt a significant correction in the dollar.
"In the upcoming weeks, one of the things to watch is the IMM positions data, which shows that the marginal yen selling in this market is disappearing," said Jan Lambregts, head of Asia-Pacific research at Rabobank in Singapore.
"That could make for quite a reversal if indeed we see a turnaround."
The euro bought around $1.1940, down from the $1.1953 fetched in late US trade on Friday but off the three-month low of $1.1875 hit last week.
Despite a bout of consolidation, the dollar gained around 1.6 percent against the yen last week while the euro slipped 1.1 percent versus the US currency.
After three lean years, the dollar has risen around 12 percent against the euro and 13 percent versus the yen this year on its widening interest rate advantage.
Still, some in the market see chances increasing that Japan and the euro zone will raise rates, which would erode the dollar's rate advantage.
ECB chief economist Otmar Issing said on Friday that central banks have to be "extremely vigilant" against inflation, prompting speculation that the ECB may raise rates sooner than later and giving the euro some support.
That was followed later in the day, however, by ECB President Jean-Claude Trichet's comment that current interest rates were still appropriate.
Traders were looking to US consumer confidence data for October due on Tuesday for signs that confidence is back on track. The key figure plunged in September, reflecting a blow to consumer confidence from hurricane damage in the US Gulf Coast and spikes in energy prices.