Sunak, the 42-year-old former finance minister, could be named leader as soon as Monday to replace Liz Truss, becoming Britain's third prime minister in less than two months.
"The United Kingdom is a great country but we face a profound economic crisis," Sunak said in a statement declaring his candidacy on Sunday.
Should she fail to hit the threshold, Sunak would become prime minister.
"He's not taking anything for granted at all," interior minister Grant Shapps, a supporter of Sunak, told BBC television.
If chosen, the former Goldman Sachs analyst would be the United Kingdom's first prime minister of Indian origin.