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The dollar rose on the first trading day of the year, as attention turned to U.S. jobs data and European inflation numbers this week which may provide clues on central banks' next moves, while bitcoin rallied.

The dollar index, which measures the U.S. currency against six rivals, was last at 101.55, up 0.17%. It fell 2% in 2023, snapping two years of gains as investors weighed the prospect of the Fed cutting rates this year.

On the other side of the dollar's ascent was the euro which dipped 0.17% as traders digested data showing euro zone factory activity contracted in December for an 18th straight month.

The Japanese yen also struggled, with the dollar up 0.43% at 141.4 yen.

A slew of economic data is due this week including European inflation data and U.S. data on job openings and non-farm payrolls, which will help shape market expectations regarding monetary policy moves from the Fed and European Central Bank.

Markets are now pricing in an 86% chance of interest rate cuts from the Fed to start from March, according to CME FedWatch tool, with over 150 basis points (bps) of easing anticipated this year.

Minutes from the last Fed meeting in December are scheduled for release on Thursday and will provide further insight into the central bankers' thinking.

"The positive sentiment from end-2023 may roll over into this week as all eyes turn to the U.S. jobs report on Friday," said Nicholas Chia, macro strategist at Standard Chartered.

That sentiment was boosting commodities and stocks on Tuesday, and rippling across into currencies.

"2024 starts in positive mood in FX," said Kenneth Broux senior strategist FX and rates at Societe Generale, pointing to commodity and stocks-associated gains in the Australian dollar - up 0.22% at $0.6825 - the Norwegian crown - slightly firmer at 10.16 per dollar - and, in emerging markets, the Mexican peso.

Rescue teams in Japan on Tuesday struggled to reach isolated areas hit by a powerful earthquake on New Year's Day, with reports of almost 50 people dead in a disaster that toppled buildings and knocked out power to thousands of homes.

Sterling was last at $1.2724, flat on the day, having clocked its strongest performance since 2017 with a 5% gain last year, although a weakening economy and election uncertainty make a repeat performance unlikely.

The crypto world started the year with a bang, with bitcoin touching a 21-month peak of $45,532 on rising expectations that the U.S. Securities and Exchange Commission will soon approve exchange-traded spot bitcoin funds.