The cuts were needed so that Greece can get a $170 billion bailout package and avoid defaulting on its debt. A default could cause losses for European banks, hurt other countries that use the euro and disrupt global markets.
The euro rose to $1.3202 in afternoon trading from $1.3170 late Friday.
"Investors are still extremely cautious about buying euros" until European finance ministers sign off on Greece's package of cuts, Kathy Lien, director of currency research for the currency trading company GFT, wrote in a note to clients.
The dollar was also weaker against other currencies. The British pound rose to $1.5774 from $1.5740. The dollar fell to 0.9157 Swiss franc from 0.9175 Swiss franc and to 99.88 Canadian cents from $1.0022 Canadian dollar.
The dollar was practically unchanged at 77.61 Japanese yen from 77.60 yen.
