BENGALURU, January 14 (Reuters) - State Bank of India, the nation's top lender by assets, has launched a new wealth management services unit, and branches to cater to start-ups, as competition with private sector rivals is rising and as its core business is seeing sluggish growth. The wealth management unit and the first bank branch for start-ups will begin operations from technology hub Bengaluru before these are expanded to other parts of the country, SBI, majority-owned by the government, said in a statement. SBI is not looking to lend to start-ups immediately but will offer advisory services such as setting up a company to taxation related issues, Chairman Arundhati Bhattacharya told a news conference. The more than two-century old bank that accounts for about a quarter of Indian bank deposits and loans is modernising its operations, growing its retail business faster and adding new segments to take on new-age private sector lenders whose profitability is higher than their state-run rivals. India was the world's fastest growing wealth management market in 2014, according to a CapGemini and RBC Wealth Management study, spurred largely by rising personal income as well as a boom in e-commerce start-ups that has also attracted marquee foreign investors.