Markey now takes 49 percent support among likely Democratic primary voters to Lynch's 32 percent support in the poll, conducted by Democratic firm Public Policy Polling. That's a slight increase since late February, when another PPP poll gave Markey a 15 percentage point lead over Lynch.

Markey, too, remains more popular than Lynch, with more than two-thirds of respondents viewing him favorably, while 18 percent of respondents have an unfavorable opinion of him. Forty-four percent of respondents view Lynch favorably, while 30 percent have an unfavorable opinion of him.

Lynch and Markey will face off in the April 30 primary, and the winner of the Democratic nomination is expected to go on and win the seat.

The poll was conducted among 496 likely Democratic primary voters from March 26-27 and has a margin of error of plus or minus 4.4 percentage points.