The euro rose to $1.3641 in the European mid-session, surpassing the previous day's high by just one pip. Trade was thin with London, the currency market's biggest trading center, closed for a public holiday.
The dollar was steady at 103.02 yen as the market digested a warning from Japanese Finance Minister Sadakazu Tanigaki that authorities would monitor foreign exchange markets over the New Year holidays.
Japan has expressed concern about the yen's export-damaging rise against the dollar, but has not conducted large-scale yen-selling intervention since March.
US consumer confidence data and a survey of manufacturing in the Chicago area are due later in the session.
So far in 2004, the dollar has shed around 8 per cent versus the euro and the British pound and 4 per cent against the yen.
Analysts had thought the $1.35 level would be a line in the sand for the European Central Bank's tolerance of euro strength, but recent comments from officials have suggested the central bank is unlikely to intervene in the near term.
On Friday, Dutch Finance Minister Gerrit Zalm said the euro's rise was still within acceptable margins, suggesting little official alarm at the pace of the single currency's gains.