European stock markets closed mixed on Tuesday as fears over Greece’s debt problems continued to make investors nervous.

The pan-European Euro Stoxx 600 index (^STOXX) ended flat, off session lows at 376.5. The Athens Stock Exchange closed down more than 2 percent with Bank of Piraeus (Athens Stock Exchange: TPEIR-GR), the National Bank of Greece and Alpha Bank (Athens Stock Exchange: ALPHA-GR) all weighing heavily on the index. London’s FTSE 100 (FTSE International: .FTSE) ended around 0.6 percent higher, the French CAC (Euronext Paris: .FCHI) closed flat, while German stocks (^GDAXI) finished 0.4 percent lower. On Monday evening, talks between Greek Finance Minister Yanis Varoufakis and his euro zone counterparts over managing the country’s debt crisis broke down. The main bone of contention seemed to be a proposal for a six-month extension of its international bailout package, which Athens described as “unacceptable.”U.S. stocks traded lower on Tuesday amid the prolonged Greece-euro zone standoff and stabilizing oil prices.

On the data front, price growth in the U.K. slowed once again in January , edging closer to deflationary territory and marking its lowest level since records began in 1989. The Consumer Prices Index (CPI) came in at just 0.3 percent in January, the Office of National Statistics (ONS) said Tuesday. This was in line with analyst forecasts but marked a move down from December’s 14-year low of 0.5 percent. The German Zew Economic Sentiment Index for February showed further improvement for the country, with a rise to 53.0 from 48.4 in January.

Read More Greece balks at bailout: What’s next? Meanwhile, fighting in Ukraine continued despite an apparent ceasefire, which also lessened investor appetite for risk. The country – ravaged by conflict between government troops and pro-Russian separatists – showed a fall in gross domestic product (GDP) fell by 15.2 percent year-on-year in the fourth quarter of 2014, according to the State Statistics Service of Ukraine on Tuesday morning.In stocks news, Danish jewelry maker Pandora (Copenhagen Stock Exchange: PNDORA-DK) surged as much as 20 percent after reporting a jump in sales in its last quarter.At the other end of benchmarks, TNT Express (Euronext Amsterdam: TNTE-NL) slipped almost 10 percent after swinging to a fourth-quarter loss. Shares of Royal Mail (London Stock Exchange: RMG-GB) also fell over 2 percent with a price target cut by Morgan Stanley. -CNBC’s Katrina Bishop contributed to this article.