The Sinn Féin leader and the PSNI Chief Constable have held a "frank" and "constructive" meeting in Washington.
Mary Lou McDonald and George Hamilton discussed their dispute over the Chief Constable's potential successor.
The meeting came after Ms McDonald said she would not have confidence in any current member of the PSNI senior command team replacing Mr Hamilton when he retires in the summer.
A spokesman for Sinn Féin said she raised the issue of the failure of the PSNI to disclose information about historical killings to Northern Ireland's Police Ombudsman.
He said Ms McDonald had raised her concerns about the matter to Mr Hamilton.
"It was a frank meeting but it was a constructive meeting as well," the spokesman said. "The big issue and where there is agreement here is that we need to remove legacy policing from contemporary policing."
The PSNI confirmed the meeting took place.
Speaking ahead of their meeting, Ms McDonald said: "We are going to meet to discuss primarily issues around dealing with legacy, the PSNI disclosing and cooperating with the police and the ombudsman and other bodies, and I think we will have a frank conversation.
"My interactions with George Hamilton have always been open and direct and I imagine that tomorrow (Thursday) will be no different."
The Sinn Féin leader's remarks about the next chief constable triggered a furore last month.
Mr Hamilton responded in robust terms, accusing her of poor leadership and suggesting she had "contaminated" and "interfered" with the selection process.
Ms McDonald's assertion, from which she has not resiled, came after she met bereaved families caught up in a controversy involving the PSNI's failure to disclose documents about killings to the Ombudsman.
The PSNI's oversight body - the Northern Ireland Policing Board - is responsible for appointing the chief constable.
Ordinarily, a Sinn Féin appointee would be on a board panel - made up of party political and independent board members - which makes the decision.
That practice was thrown into doubt following Ms McDonald's remarks, for a time raising the prospect of a panel without Sinn Féin representation, or without any political appointees at all.
But, after taking legal advice, the Policing Board ultimately decided to press ahead with a panel featuring political representatives, including Sinn Féin.