By Kevin Buckland

TOKYO (Reuters) - Japan’s Nikkei share average rose 1% on Friday to clock its best week in three months, as investors turned more hopeful that U.S. President Donald Trump would be able to broker trade deals with some of its top trading partners, including Japan.

The Nikkei touched a two-week high of 34,758.97 before ending the day up 1.03% at 34,730.28, despite somewhat muted trading due to the Easter holidays in most other markets.

The broader Topix added 1.14%.

The Nikkei climbed 3.41% for the week - the most since January 20 - to snap a three-week losing run.

On Thursday, Trump and close ally Italian Prime Minister Giorgia Meloni expressed optimism about resolving U.S.-European Union trade tensions. Trump also signalled a potential end to tit-for-tat tariff hikes with China.

A day earlier, Japan’s top negotiator, economy minister Ryosei Akazawa, kicked off dialogue in Washington, and told reporters afterwards that Trump had said getting a deal with Japan was a "top priority". Trump hailed discussions with Japan on social media, saying "Big Progress!"

"The mood seemed overall quite positive, underscored by Trump’s social media post featuring a smiling photo of him with Akazawa in the Oval Office," said James Brady, vice president at advisory firm Teneo.

"The general sense is that the discussions got off to a reasonable start."

Shipping was the second-best performer among the Tokyo Stock Exchange’s 33 industry groupings, gaining 2.92%.

Pharmaceuticals topped the list with a 4.68% jump, led by a 17.54% surge for Chugai Pharmaceutical after an obesity drug it developed and licensed to Eli Lilly (NYSE:LLY) performed well in clinical trials.