Wall Street's volatility index on Tuesday dropped further away from 50 points amid a broader rebound in equities as hopes grew that the U.S. might enter into trade negotiations with some countries.

U.S. President Donald Trump said Monday his administration won't pump the brakes on imposing tariffs on products coming into the U.S., but he’s open to discussing trade deals with other countries.

The Cboe Volatility Index (VIX) fell -8.5% to 42.97 points. The VIX (VIX) had briefly topped 50 points on Thursday. 

The CNN Fear & Greed Index, however, slipped further into the Extreme Fear territory.

"Admittedly, Trump did sound open to reaching deals with other countries, saying in his message on China tariffs that 'Negotiations with other countries, which have also requested meetings, will begin taking place immediately,'" Deutsche Bank's Henry Allen added.

The sentiment across markets was broadly better on Tuesday, with U.S. stock index futures higher;  Asia-Pacific stocks also rebounded, and European markets recovered on hopes that U.S. may soften tariff stance