TOKYO, Sept 10 (Reuters) - Japan's Nikkei hit a six-month high on Friday and the broader Topix index touched its best level since 1990, extending their bull run since the end of August on hopes for a new government and further improvement in earnings.

The news that U.S. President Joe Biden and Chinese counterpart Xi Jinping had held talks on the phone also supported the rally by easing concerns about simmering Sino-U.S. tensions.

The Nikkei average rose 1.13% to 30,347.41, while the Topix gained 1.07% to 2,087.08.

Hopes that a new leader at Japan's dominant ruling party would compile an economic stimulus and secure a decisive election victory have boosted shares prices after unpopular Prime Minister Yoshihide Suga offered to resign last week.

Japan's corporate earnings outlook has also been improving of late as the country's vaccine roll-outs move closer to catching up with other developed nations.

Financial sectors were among the top gainers after SBI Holdings announced an offer to buy a near majority stake in Shinsei Bank in an unsolicited bid to take effective control of the lender.

SBI rose 7.1% while Shinsei Bank was untraded with glut of buy orders at its daily limit price, which was 20.8% above Thursday's close.

The brokerage index rose 2.6% while banks added 1.8% as SBI's move sparked hopes of more consolidation in the industry.

On the other hand, Eisai lost 8.4% after Biogen Inc shares tumbled after it said the launch of its Alzheimer's drug, which the two firms have developed, was slower than what was initially anticipated.

Nipro shed 7.8% after the medical equipment firm announced the sale of 30 billion yen ($273.47 million) in convertible bonds, which could cause a 13% dilution. ($1 = 109.70 yen) (Reporting by Hideyuki Sano; Editing by Devika Syamnath)