The Unites States allowed Huawei Technologies to buy U.S.-made goods to maintain existing networks and provide software updates to existing Huawei handsets until Aug. 19 after blocking it from buying U.S. goods last week.
The pan-European STOXX 600 gained 0.5%, with Germany's trade-sensitive DAX rising 0.9%. London-traded stocks pared gains as the pound firmed on Prime Minister Theresa May's comments about the next Brexit votes.
"I think the easing up on Huawei is being seen as a sign that while the United States and China are unhappy with each other, neither side wants to burn the negotiation bridge at the moment," said Connor Campbell, an analyst at Spreadex in London.
The tech sector rose 1.6%, making back a chunk of Monday's 2.8% slide. Chipmakers Infineon Technologies , AMS and STMicroelectronics gained between 1% and 4.2%.
Telecom Italia rose 2.3% as it posted first quarter results and confirmed its guidance for the next three years. The firm's chief executive said it was in touch with five banks over plans to create a joint venture to offer consumer credit services.
Italy's biggest phone group reported a "solid set of results", with core earnings beating the consensus expectation of analysts, Deutsche Bank said in a note.
Norsk Hydro climbed 5.6% as a Brazilian federal court allowed the Oslo-traded firm to resume full output at the world's largest alumina refinery for the first time in more than a year.
Oil and gas stocks added 1%, with Vestas Wind Energy leading the gains with a 3.9% rise. The Danish firm secured an order from Finland's Fortum for a 90 megawatt wind project and launched a wind turbine targeting the U.S. market.
Banks rose 0.7%, lifting off Monday's more-than three-month closing low.
As risk appetite crept back into markets, defensive stocks in sectors such as telecommunications underperformed.
However, stocks are not yet out of the woods, still plagued by investor uncertainty regarding the U.S.-China trade war.
"We've had a very powerful rally (year-to-date) and if there is a continued escalation or a failure to resolve where we go from here, there is certainly downside in equity markets," said Simon Webber, lead portfolio manager on the global & international equities team at Schroders.
(Reporting by Aaron Saldanha,; and Amy Caren Daniel in Bengaluru; Josephine Mason in London)
By Aaron Saldanha