The pan-European STOXX 600 <.STOXX> jumped 0.8 percent at the open but quickly trimmed gains to trade up 0.4 percent by 0930 GMT.
Germany's DAX <.GDAXI> hit a session low after GDP figures showed the German economy grew by 1.5 percent in 2018, the weakest rate in five years, though it managed to avoid a technical recession.
Overall economic sentiment in the euro zone has slumped over the past months, with the European Commission's sentiment indicator falling to its lowest ebb since 2012 in December.
Sectors reliant on trade and exports to China, such as tech, industrials, basic resources, and autos, were the top gainers on Tuesday though they pared gains fast after the open.
Some investors were doubtful this stimulus would have much impact on European exporters.
"To give a real boost to European exporters, we would need more than just an announcement on tax cuts, we would need commitments to infrastructure investment (from China)," said Martin Moeller, co-head of Swiss and global equity portfolio management at Union Bancaire Privee in Geneva.
The autos sector <.SXAP> jumped to its highest since Dec. 5 on the stimulus news and after a strong update from Peugeot maker PSA Group soothed investors' concerns about carmakers facing slowing demand in China.
Shares in the French carmaker climbed to their highest since mid-November after reporting record sales for 2018. The stock pared gains fast, though, trading up just 0.2 percent by 0930 GMT.
Italian banks sold off, dragging Milan's FTSE MIB <.FTMIB> down into negative territory, down 0.2 percent.
Italy's biggest lenders Unicredit and Intesa Sanpaolo fell 2.8 and 1.8 percent after a report in Il Sole 24 Ore that the European Central Bank has asked lenders to fully cover impaired loans by around 2026.
UBI Banca, Banco BPM and BPER also fell 3.8 to 6.7 percent, the biggest Italian fallers.
"If things get much worse (for Italian banks) the ECB will come and help - I think they will consider a second round of targeted refinancing operations," said UBP's Moeller.
"But before you get this the share prices might come down significantly from here," he added.
M&A was a driver with Swedish telecoms company Millicom up 4.7 percent after a bid from Liberty Latin America.
Kinnevik, the majority stakeholder in Millicom, rose 3 percent among top STOXX gainers.
Chocolate maker Lindt & Spruengli fell 2.8 percent after reporting sales rose 5.1 percent in 2018, in line with its goal, but highlighted the market environment remained "very challenging".
(Reporting by Helen Reid; Editing by Josephine Mason and Alison Williams)
By Helen Reid
Stocks treated in this article : Peugeot
, Euro Stoxx 50
, Stoxx Europe 600
, Intesa Sanpaolo
, Lindt & Spruengli
, UBI Banca
, GVC Holdings
, Millicom International Cellular SA(SWE)
, William Hill
, Liberty Global LiLAC
, Banco BPM
, UniCredit SpA
, Liberty Latin America
, STOXX ITALY 45 (EUR)