Domestic stock markets started Tuesday's session on a lacklustre note amid weakness in Asian peers. The Sensex fell as much as 136.87 points to touch 35,926.94 on the downside, and the Nifty declined to 10,817.00, down 46.5 points from the previous close. Losses in information technology stocks offset the advances in energy and metal shares. Meanwhile, the rupee edged higher to 70.81 against the US dollar in early trade, from its previous close of 70.92 against the greenback.