NEW DELHI—An aide to jailed Indian activist Anna Hazare said the anticorruption advocate had reached a deal with police early Thursday under which he would leave detention and stage his planned hunger-strike protest in the capital for up to 15 days.

The tentative word came after several thousand people gathered in central Delhi and other Indian cities on Wednesday evening in support of Mr. Hazare, 73 years old, who was jailed on Tuesday after refusing to agree to conditions on his proposed hunger strike to call for a more...