NEW YORK (AFP) - Under fire for using private e-mail while secretary of state, Mrs Hillary Clinton, the likely next Democratic presidential nominee, said on Tuesday she did so for "convenience" - but admitted this was probably a mistake.

Mrs Clinton insisted the private server that she used suffered no security breaches and that she discussed "no classified material" in the e-mails, while promising she had turned over all work communications to the State Department and wants to see them made public.

But she also admitted she deleted roughly 30,000 personal e-mails - such as those planning her daughter's wedding, her mother's funeral and "yoga routines". And, in a move not calculated to silence her critics, she said the Clinton family server on which all her e-mails were stored would not be turned over to the government.

Mrs Clinton said it had been "a matter of convenience" to use a personal e-mail system on the job and insisted she had taken "unprecedented" steps to comply with the law requiring official records be kept.

"Looking back, it would have been better for me to use two separate phones and two e-mail accounts," Mrs Clinton told reporters after speaking at a United Nations women's conference.

After she left office, she said, "we went through a thorough process to identify all of my work-related e-mails and deliver them to the State Department." But she offered no avenue for proving that potentially embarrassing work-related e-mails were not permanently deleted.

Asked directly if she or her team destroyed any work e-mails, she said "we did not". The former first lady and US senator has been accused, mainly by her Republican opponents, of trying to improperly keep her e-mails out of the public domain.

While Mrs Clinton apparently contravened State Department rules against conducting official business on personal e-mail, she insisted her actions were legal.

The 20-minute appearance was her first before a swarm of reporters since the e-mail revelations last week, and has been widely described as an effort for the famous Democrat to tamp down the uproar before she launches a run for the 2016 White House race, perhaps as early as April.

But Republicans kept up the pressure, demanding the entirety of Mrs Clinton's correspondence, reportedly from a clintonemail.com address, be considered for release.

CALLED TO TESTIFY

"Secretary Clinton didn't hand over her e-mails out of the goodness of her heart - she was forced to by smart, determined, and effective oversight by the House Select Committee on Benghazi," House Speaker John Boehner's spokesman said, referring to the panel investigating the terror attacks in Libya in 2012 that killed four Americans.

The committee's chairman Trey Gowdy said Mrs Clinton's comments provided more questions than answers.

"Without access to Secretary Clinton's personal server, there is no way for the State Department to know it has acquired all documents that should be made public," Mr Gowdy said in a statement.

"I see no choice but for Secretary Clinton to turn her server over to a neutral, detached third-party arbiter who can determine which documents should be public and which should remain private."

Mr Gowdy also said he would urge Mrs Clinton to appear twice before his committee, first to "clear up her role and resolve issues surrounding her exclusive use of personal e-mail," and then in a public hearing on Benghazi.

Mrs Clinton had come under mounting pressure to address the issue, which Republicans have seized on as a sign Mrs Clinton may have sought to keep sensitive e-mails private despite her official communications being part of the public record.

She has already turned over around 30,000 e-mails to the State Department.

The process of publicising the e-mails will take months, but State said on Tuesday it would soon release a first batch.

"I'm very glad to hear (that), because I want it all out there," Mrs Clinton said.

President Barack Obama threw cautious support behind his former cabinet member at the weekend but stressed the need for transparency in his administration.

On Monday, White House spokesman Josh Earnest said Mr Obama and Mrs Clinton "did have the occasion to e-mail one another", but said the President "was not aware of the details" of her private e-mail account or server.