TOKYO, June 21 (Reuters) - Japan's Nikkei climbed on Tuesday after falling to a three-month low in the previous session, as investors scooped up beaten-down cyclical stocks, while U.S. futures pointing to a higher open and overnight gains in European shares also boosted sentiment.

The Nikkei share average was up 1.76% at 26,225.15, as of the midday break, extending gains above the psychological 26,000 mark as the morning progressed. It had dipped to a low of 25,520.23 at the start of the week for the first time since March 16.

The rally on Tuesday was broad-based, with 211 of the Nikkei's 225 components rising, while 13 fell and one traded flat.

The broader Topix advanced 1.67% to 1,849.27.

U.S. stock markets, which were closed on Monday for a holiday, looked set to rise, with S&P 500 e-mini futures up 1.39%. European stocks gained overnight, with the pan-European STOXX 600 index finishing 1.0% higher.

"The strong rise in U.S. futures is boosting market mood," said a market participant at a domestic securities company. "For today, stocks look like they'll stay positive."

Cyclical stocks rebounded after Monday's fall. Japan Airlines and rival ANA Holdings rallied 3.81% and 3.26%, respectively. Uniqlo store operator Fast Retailing added 1.3%.

Tech also had several big winners. Sony Group jumped 3.31%, while startup investor SoftBank Group advanced 3.45%.

Automakers were firm, with the yen hovering near its weakest level in more than two decades. Toyota gained 1.65% and Nissan rose 2.91%.

The best performing sector on the Nikkei was energy, which rallied 3.46% amid higher crude oil prices. Defensive utilities trailed, but were still higher by 0.20%. (Reporting by Tokyo markets team; Editing by Subhranshu Sahu)