Oil prices climbed on Monday as optimism about a strong rebound in fuel demand in developed countries and China in the second half of the year overshadowed growing concerns of a full lockdown in India to curb the COVID-19 pandemic. Brent crude futures for July gained 36 cents, or 0.5%, to $67.12 a barrel by 0045 GMT while US West Texas Intermediate for June was at $63.94 a barrel, up 36 cents, or 0.6%.