The US on Monday issued a new 90-day extension allowing US companies to continue engaging in business with China's Huawei Technologies. However, CNBC's report that China was pessimistic regarding the signing of the trade deal dampened sentiment.
The STOXX 600 index gained 0.4% with shares in London leading gains.
Meanwhile, Germany's TLG Immobilien rose 2.6% following the announcement of an all-stock merger with Aroundtown SA.
Auto companies also recovered after getting beaten down on Monday after data indicated that passenger car registrations in Europe increased to their highest level in October in a decade, thanks to demand in Germany and France.
Elsewhere, Asian shares ended muted with the unrest in Hong Kong being closely watched by market participants. A Hong Kong University campus stand-off between anti-government protesters and police is not in its third day, CNBC reported.
Focus now remains on any developments in the trade deal, political campaining in the UK, and the situation in Hong Kong.