* FTSEurofirst 300 falls 0.6 pct after 2 positive sessions
* Shares of oil companies come off highs after oil deal
* Banks under pressure as JP Morgan suggest not to buy (Adds details, updates prices)
By Danilo Masoni and Sudip Kar-Gupta
MILAN/LONDON, Feb 16 (Reuters) - European shares fell on Tuesday after two sessions of strong gains, with disappointment over a deal to tackle a global oil supply glut weighing on sentiment.
The pan-European FTSEurofirst 300 index fell 0.6 percent by 1454 GMT, reversing initial gains and following a 6 percent rise made over the last two sessions. Euro zone's blue-chip index Eurostoxx 50 index fell 0.49 percent.
Top oil exporters Russia and Saudi Arabia agreed on Tuesday to freeze output levels, but said the deal was contingent on other producers joining in -- a major sticking point, with Iran absent from the talks and determined to raise production.
"This agreement needs the nod from other OPEC and non-OPEC nations, which seems unlikely," said Stephane Ekolo, Chief European Strategist at Market Securities. "Therefore market participants turned cautious again and risk-off sentiment is back on."
The decision, which pushed crude oil prices down, comes after more than 18 months of declining oil prices in which benchmark crude futures prices have dropped by two-thirds on concerns about oversupply and a slowing global economy.
Shares in oil stocks came off highs but most remained in positive territory. BP and Total advanced 1.6 percent and 0.4 percent respectively, while Eni fell 0.75 percent.
Francois Savary, chief investment officer at Geneva-based Prime Partners, said he believed oil prices will rise further down the road, adding that his stocks in the sector were Total and Exxon, while BP is also interesting.
Banks were led lower by Standard Chartered, which fell 6.2 percent after several brokerages cut their target prices following a recent rally.
Elsewhere in the sector, Commerzbank and Deutsche Bank fell 2 and 0.7 percent respectively. Some brokerages cut their target prices on both stocks with traders saying the recent gains were overdone.
Along with other Italian banks, Monte dei Paschi managed to reverse initial losses and was last up 10.3 percent. Some investors said the stocks offered attractive valuations but caution over the sector remained.
JP Morgan analysts said they would not buy into the European banking sector, given pressures on banks' profitability from negative interest rates and weak financial markets.
The FTSEurofirst remains down by 11 percent since the start of 2016, because of worries over a global economic slowdown and the health of Europe's banking sector.
Shares in Vodafone slipped 0.2 percent after the British phone network operator agreed to combine operations in the Netherlands with Liberty Global, with Vodafone paying 1 billion euros in cash to Liberty.
Shares in Telecom Italia fell 4.7 percent after its quarterly core profit missed expectations.
Today's European research round-up (Editing by Hugh Lawson and Katharine Houreld)