(CNN) Sen. Elizabeth Warren called on Pete Buttigieg to open up his private fundraisers to reporters and reveal the clients he worked with during his time at McKinsey, the management consulting firm, after a speech on Thursday in Boston.

Warren, who rarely goes after her rivals by name, has mostly steered clear of responding to Buttigieg's own criticism of her policy proposals and only addressed the South Bend, Indiana, mayor directly in response to questions after a speech at a Democratic National Committee fundraiser.

The escalation of a simmering clash between the candidates could mark a new phase of the Democratic primary campaign. Buttigieg, who is leading Iowa and rising in recent national polls, has been critical of both Warren and Sen. Bernie Sanders, but mostly escaped any significant pushback from either campaign. That changed on Thursday, when Sanders in a separate interview on MSNBC also shot back at Buttigieg's recent swipes at his and Warren's tuition-free public college plans.

Questions over Buttigieg's record with McKinsey were brought front and center earlier in the day when the New York Times editorial page said his continued refusal to talk about his work there was no longer "tenable" and that he "owes voters a more complete account of his time at the company." Buttigieg has said his silence is mandated by a nondisclosure agreement, which he is seeking to be released from.

Asked whether she agreed with the Times' request, Warren said she did before launching into a wider call for transparency from Buttigieg, who has not made his big donor fundraisers open to media.

Read More