The survey showed the Conservatives had the support of 46% of likely voters in the June 8 election, ahead of Labour on 24%, the Liberal Democrats on 11% and the UK Independence Party on 8%.
The poll was the first in a new series of polls to be conducted by Kantar and therefore had no comparative figures for how support for the parties had changed.
Kantar interviewed 1,196 people online between April 20 and 24.
The poll also suggested that Conservative voters were more enthusiastic in their support for their party than Labour voters were for theirs, Kantar said.
ICM interviewed 2,024 adults between April 21 and 24. Polls have suggested that May is on course for a sweeping victory which could extend her majority in parliament to more than 100 seats.