By Patrick Graham

LONDON (Reuters) - The dollar steadied after breaking past more of last year's peaks against the euro on Thursday, with only the March 2015 high of $1.0457 standing in the way of a push toward parity that banks are again saying is on the cards.

With U.S. markets out for the Thanksgiving holiday, trade was already thinning out after the dollar set a series of new landmarks in early trade in Europe, extending its surge after another strong batch of U.S. economic data on Wednesday.

The dollar hit an eight-month high against the yen and an almost 14-year high against a basket of currencies that measures its broader strength.

It also notched up new record highs overnight against a raft of emerging market currencies including the rupee <INR=>, the lira <TRY=> and China's offshore yuan. <CNH=D3>

"It is tempting to take profit given the U.S. will be absent later, but there is no change in the fundamental view on the dollar," said Valentin Marinov, head of G10 strategy at Credit Agricole in London.

"It does feel like clients are steadily becoming more confident in the dollar rally. They have focused on the positives from the U.S. election and the data we have seen suggests there is more room for U.S. yields to rise."

The dollar's surge is based largely on a belief that Donald Trump's presidency will witness a bump in inflation that will drive U.S. interest rates higher and potentially see substantial dollar capital brought home by U.S. corporates.

That would appear to play into the hands of European, Japanese and Chinese policymakers, who hope weaker currencies will help deal with their respective problems with growth.

But it also risks choking off any broader upturn.

"Further dollar appreciation will go hand in hand with a tightening of global financial conditions. That is the big risk," Marinov said. "The optimism about Trump risks choking off any boost to growth before he has even started."

Turkey's central bank raised interest rates for the first time since 2014 on Thursday, reacting to a 14 percent fall in the lira this year.

Traders reported Chinese state-owned banks selling dollars to support the yuan as it inched toward 7 per dollar, a level not seen in eight years.

Among developed markets, it is the yen that has taken the biggest hint since Trump's election. It was down another half a percent at 113.03, having reached 113.53 earlier.

The euro steadied at $1.0573 after hitting lows of $1.0518 while the dollar index also steadied at 101.57, just off the morning high of 102.05. <.DXY>

But its slide in the past week has given heart to long-term dollar bulls like Deutsche Bank and Goldman Sachs, and other banks are signing up to the idea that parity with the dollar is back on the table.

"Downward momentum for the euro against the U.S. dollar remains firmly in place in the near-term," said Lee Hardman, a currency analyst with MUFG in London. "A break below $1.0458 would open the door for a potential test of parity. The euro is likely to remain offered in the week ahead."

(Additional reporting by Tokyo markets team; Editing by Mark Heinrich)