The euro rose against the dollar but was down versus sterling.
Oil prices rebounded meanwhile, after slumping Friday to the lowest levels in more than one year.
Bitcoin extended its slide, dropping under $4,000 to $3,675.44 — the lowest level for 14 months.
“Italian stocks have been the outperformer in Europe… on reports that the government may consider reducing its deficit target in a bid to avert a disciplinary procedure in Brussels and a backlash in the markets,” noted Craig Erlam, senior market analyst at Oanda trading group.
“The pound is also a little higher… after (British Prime Minister) Theresa May overcame the first, and smallest, hurdle to her Brexit deal getting over the line.”
May convened her cabinet and will update Britain's parliament on the newly-agreed Brexit deal Monday, as she begins the tricky task of selling the plan to her sceptical country.
In Rome, Italy's populist government appears open to reducing its draft budget deficit, fuelling a surge in the Milan stock market on hopes Rome could ease a stand-off with EU officials in Brussels.
Around 1430 GMT, Milan's FTSE MIB was up 2.5 percent compared with the close on Friday. London's FTSE 100 gained 0.8 percent.
Most Asian stock markets closed higher as investors tentatively picked up cheap stocks, with focus on an expected meeting between US President Donald Trump and his Chinese counterpart Xi Jinping at the weekend that will be watched for signs of a softening in the China-US trade war.
Those gains came despite more selling of shares in Asian energy firms following another collapse in oil prices Friday.
Wall Street also pushed higher at the opening bell, with the Dow climbing 0.6 percent.
The more positive mood comes at the start of a week set to include a speech by Federal Reserve boss Jerome Powell and the release of the bank's last policy meeting minutes, before culminating in a G20 gathering in Buenos Aires.
While the summit will focus on several global issues, the meeting between Trump and Xi will get the most attention, with the economic superpowers engaged in a trade war just as global growth starts to stutter.
Expectations for a deal to end the standoff are low, however.
Oil prices enjoyed a bounce but remain well beaten down after Friday's hammering, which saw WTI sink 7.7 percent and Brent lose more than six percent.
The commodity has plunged by about a third in value from four-year highs in early October owing to a range of issues, including a global economic slowdown, the trade row, rising crude supplies, softer-than-expected US sanctions on Iran, stuttering business activity in China and a stronger dollar.
All eyes are now on a meeting of the Organization of the Petroleum Exporting Countries on December 6 to see if the cartel will cut output.