The euro fell on weak US jobs data late last week, while the dollar steadied against a currency basket. Traders were wary of chasing the dollar lower with US markets closed on Monday for Independence Day.
Chris Turner, head of foreign exchange strategy at ING said: "The market last week was clearly concerned about a US slowdown… It was the first week in a long time we have seen the dollar react like that. There is a creeping fear that the strong dollar environment will start to break. That has not happened yet and it is likely to be steady this week."
The euro eased 0.3 percent to $1.2522. The euro fell 0.4 percent versus the yen on corporate selling. The euro briefly rose 10 pips to around $1.2545. The dollar was flat against the yen at 87.74.