Romney has asserted that a 1997 decision by the Massachusetts state supreme court means that while paper records of his administration are property of the state, they are exempt from public disclosure.
But the state had allowed access to some of the estimated 600 boxes of paper records from Romney's governorship held by the state archives.
The surge in requests to review the records comes after reports that Romney spent nearly $100,000 in state funds to replace computers in his office at the end of his term as part of an unprecedented effort to keep his records secret.
The move during the final weeks of Romney's administration was legal but unusual for a departing governor, Massachusetts officials say.
The effort to purge electronic records was made a few months before Romney launched an unsuccessful campaign for the Republican presidential nomination in 2008. He is again competing for the party's nomination, this time to challenge Barack Obama for the presidency in 2012.
The requests to see the paper records and continuing questions about the public disclosure law prompted Massachusetts state officials last month to briefly impose a moratorium on access to the records.
But later they relented and allowed access to about 20 percent of records that previously had been opened for public inspection.
On Tuesday, Brian McNiff, a spokesman for Massachusetts Secretary of State William Galvin, the elected official in charge of the state archives, said that officials are still reviewing the law as it relates to Romney's records, but have decided that they will now allow journalists and the public to request access to any boxes of records that had not previously been released.
However, nonpolitical archivists will review and redact the records before any are made public, McNiff said.
At a campaign appearance Tuesday in Paradise Valley, Arizona, Romney said his office had sent the state archives "all that was required under the law."
Republican and Democratic opponents of Romney say the scrubbing of e-mails and the claim that his paper records are not subject to public disclosure hinder efforts to assess his performance as a politician and elected official.
Five weeks before the first contests in Iowa, Romney has seen his position as frontrunner among Republican presidential candidates whittled away in the polls as rival Newt Gingrich, the former speaker of the House of Representatives, has gained ground. (Reporting by Mark Hosenball in Washington; Editing by Philip Barbara)
