The Tory leader said she would fight for every vote on 8 June to strengthen her hand in Brexit talks.
Labour leader Jeremy Corbyn said his party faced a challenge on a "historic scale" to win back power, but insisted he could close the gap on the Tories.
The Tories gained 500 seats and seized control of 11 councils.
It was the best local election performance by a governing party in 40 years, with the gains mostly coming at the expense of Labour and UKIP, which lost all of its 145 local authority seats.