Italian Deputy Prime Minister Matteo Salvini, whose far-right League triumphed in European elections on Sunday, said the European Commission could fine Italy 3 billion euros for breaking EU debt and deficit rules, a comment which weighed on the single currency.
Pro-Europe parties kept a majority of seats in European parliamentary elections, with support growing for eurosceptic and right-wing parties but not as much as investors had feared.
European leaders now meet in Brussels to begin the process of filling a number of top EU posts, from the head of the European Commission to the European Central Bank.
Another potential battle between Brussels and Rome over Italy's spending plans is likely to keep the euro under pressure, analysts said, citing the link between rising Italian government bond yields and the single currency's weakness.
"The League did fairly well. Someone like Salvini will see that as a mandate to continue doing what he is doing," said Neil Mellor, currencies analyst at BNY Mellon. "We need to hear soothing words from the ECB (European Central Bank) for all to be well."
The euro slipped 0.1pc to $1.1179, but remains above two-year lows of $1.1105 hit last week.
Broader moves in foreign exchange markets remain small amid uncertainty over how trade tensions between the United States and China are affecting the world's major economies.
The dollar rose 0.2pc against a basket of peers, its index touching 97.787. It remains off a two-year high of 98.371 hit on Thursday.
The yen rose 0.2pc to 109.32 yen as US President Donald Trump visited Japan.
On trade, Trump said on Monday he expected the two countries to be "announcing some things, probably in August, that will be very good for both countries", although he has also put pressure on Tokyo to cut Japan's large trade surplus with the United States.
Dollar traders are now preparing for US consumer confidence numbers for May, due at 1400 GMT.
"Negotiating from a position of strength remains President Trump's modus operandi and that should be supported today with another strong US consumer confidence release for May.
We expect the US to maintain trade pressure on China and are not looking for any immediate resolution," analysts at ING said.
The Swedish crown rallied 0.4pc to 10.673 crowns per euro despite deteriorating consumer and manufacturing sentiment, as inflation was also predicted to increase against earlier expectations.
Sterling, hurt on Monday by the poll-topping performance of the Brexit Party at the expense of Britain's governing Conservatives in European parliamentary elections, slipped another 0.2pc to $1.2656.
Bitcoin, the world's biggest cryptocurrency, stabilised after soaring to new one-year highs.
The price of Bitcoin stood at $8,704 after hitting $8,939 on Monday. The virtual currency has rocketed more than 130pc in 2019.