* Fed shift last week hurts dollar demand

* Euro highest since May 2018, dollar at new low

* China’s yuan soars to more than one-year high

* Graphic: World FX rates in 2020 tmsnrt.rs/2RBWI5E

LONDON, Sept 1 (Reuters) – The euro homed in on the $1.20 mark on Monday as it scaled another 28-month high while the dollar weakened to a new multi-year low as investors bet the Federal Reserve’s new policy framework meant U.S. rates would stay low for longer.

The euro reached as high as $1.1997 in Asian trading hours, its highest since May 2018 and leaving it up 7.5% in three months.

The Fed’s announcement last week that it would tolerate periods of higher inflation and focus more on average inflation and higher employment has encouraged traders to sell the dollar.

U.S. political uncertainty ahead of November’s presidential election and concerns about the pace of the recovery in the United States’ economy have also weighed on the greenback, with the euro the biggest beneficiary.

While analysts will be watching euro zone inflation data due later on Monday after Italian inflation weakened, ING analysts said “no imminent response from the ECB (European Central Bank) is likely and as the U.S. dollar outlook remains unappealing, the bias remains for higher EUR/USD this week”.

The euro was last up 0.3% at $1.1968.

The dollar index – which measures the U.S. currency against a basket of rivals – was down 0.2% at 91.954 after earlier hitting its lowest since April 2018.

The U.S. data calendar this week is full of important releases on manufacturing, durable goods and employment, but positive results are unlikely to halt the dollar’s decline due to expectations that U.S. rates will remain extremely low.

The Chinese yuan brushed off concerns about diplomatic tension over Taiwan to surge to its strongest in more than a year against the greenback.

In offshore markets, the dollar fell 0.5% against the yuan to 6.8135.

Viraj Patel, an FX and Global Macro strategist at Arkera, said China’s yuan rallying was a “sign of strong capital inflows”.

“But Beijing’s also allowing $USDCNY to move lower to avoid attention from the White House over its FX policy,” he added.

Elsewhere, the British pound gained 0.4% to $1.3422, the highest since December, helped by dollar weakness and after Japan’s foreign minister said a broad agreement on a Japan-UK trade deal was close.

The dollar was quoted at 0.9014 Swiss francs, a shade above the lowest in more than five years.

Against Japan’s currency the greenback eased 0.2% to 105.74 yen.

The yen had jumped last week after Japanese Prime Minister Shinzo Abe resigned on health grounds.

The Australian dollar rose 0.2% to $0.7395, close to its highest since August 2018.

The RBA left its cash rate at a record low of 0.25% on Tuesday but surprised investors by expanding a programme of cheap funding for banks and extending it out to mid-2021. (Additional reporting by Stanley White in Tokyo, editing by Ed Osmond)