By Ankur Banerjee and Stefano Rebaudo

(Reuters) - The U.S. dollar clung to a 2-1/2 month high on Tuesday on expectations the Federal Reserve will take a measured approach to interest rate cuts, while a too-close-to-call U.S. election campaign kept investors on edge.

The dollar's strength, boosted by rising Treasury yields, kept pressure on the yen, euro and sterling, a theme that has been building over the past few weeks as traders scale back their bets on rapid U.S. rate cuts.

Some analysts argued that the release of the Beige Book late on Wednesday could be the biggest threat to the greenback this week, with the previous summary of economic conditions seen by some as the main trigger for the 50 bp rate cut in September that kicked off the Fed's easing cycle.

Four Fed policymakers expressed support on Monday for further rate cuts, but appeared to differ on how fast or far they believe any cuts should go.

Markets are pricing in an 87% chance of the Fed cutting rates by 25 basis points (bps) next month, versus a 50% chance a month earlier, when investors saw an equal likelihood of a larger 50 bp cut, the CME FedWatch tool showed.

Traders are anticipating another 40 bps of easing overall for the rest of the year.

"The U.S. exceptionalism story remaining intact and what Fed speakers are hinting at are gradual rate cuts from here," said Charu Chanana, chief investment strategist at Saxo. "This, together with the betting odds of a Trump 2.0 picking up, has brought another leg of gains for the U.S. dollar."

The dollar index, which measures the U.S. currency versus six others, was last at 103.87, having touched 104.02 on Monday, its highest since Aug. 1. The index is up more than 3% so far this month.

The euro last bought $1.0827, near its lowest since Aug. 2, while sterling was at $1.3006, near its lowest since Aug. 20.

Euro zone PMI data on Thursday could provide an additional downward push to the single currency if it underlines the poor economic situation in the euro area and boosts bets on future European Central Bank rate cuts.

ECB speakers will also be in focus after President Christine Lagarde delivered a dovish message last week.

"The key question is: are the hawks fine with Lagarde’s sanguine disinflation view, a gradual shift in focus to growth and such a dovish market pricing?," said Francesco Pesole forex strategist at ING.

"Given some lingering pockets of sticky services inflation in the euro zone, the answer is probably no."

ELECTION IN FOCUS

With the U.S. election just two weeks away, the rising odds of former President Donald Trump winning are boosting the dollar, since his proposed tariff and tax policies are seen as likely to keep U.S. interest rates high.