Theresa May has insisted the inquiry into child sexual abuse in England and Wales will not be scaled back despite recent setbacks.
The prime minister said she and Home Secretary Amber Rudd still had confidence in the inquiry.
She spoke after the lead counsel to the hearings, Ben Emmerson, was suspended on Wednesday and the inquiry's second most senior lawyer resigned.
Elizabeth Prochaska's resignation is said to be not linked to recent events.
Ms Prochaska told BBC Newsnight's programme: "I can confirm that after 15 months working on the Independent Inquiry into Child Sexual Abuse, I resigned from my position as junior counsel with effect from 15 September 2016.
"I very much valued the experience of working with the inquiry and I wish all my former colleagues the best as they continue their work."
Her resignation from her role as first junior counsel follows other problems faced by the inquiry, which was originally set up in 2014.
On Wednesday the inquiry said it had "recently become very concerned about aspects of Ben Emmerson QC's leadership" of his team and he had been suspended so these could be properly investigated.
The BBC understands more than one complaint has been made against him.
Preliminary hearings for the inquiry began in March at the Royal Courts of Justice in London.
But Prof Alexis Jay, the current chairwoman, is the fourth person to have been appointed to lead the inquiry, following three earlier resignations.
Prime Minister Theresa May said the "really important" hearings would go ahead as planned.
Speaking during a visit to Wiltshire, she said: "I set the inquiry up when I was home secretary and the current home secretary has made clear the original terms of reference were the right ones and I think that's important.
"We should always remember why it is that the inquiry was set up in the first place and when those terms of reference were set they were agreed with victims and survivors and it is victims and survivors who are at the heart of this inquiry."
In a statement, the inquiry thanked Ms Prochaska for her "commitment" and "the valuable contribution that she made to its work".
It also described the recent events as "unsettling, particularly for victims and survivors of child sexual abuse and all those who are engaged with the inquiry's work".
The inquiry added: "It has been said that the inquiry is in crisis. This is simply not the case, and the chair and panel are united in their determination to see this important work through to a conclusion."
The inquiry was set up to examine whether public bodies including the police have failed in their duty to protect children from sexual abuse. It will also examine claims of abuse involving "well-known people".