NEW YORK, May 22 (Reuters) - The U.S. Securities and Exchange Commission said on Friday it would toughen rules on stock trading by its employees, following a probe of possible insider trading involving two lawyers at the agency.

The new rules, which must be approved by the Office of Government Ethics, would require SEC employees get preclearance for all securities trades.

Employees also would be barred from trading in securities of companies under SEC investigation regardless of whether they have any knowledge of the probe.

"These measures will further bolster our standing by helping to prevent not only an actual impropriety, but the appearance of one as well," Chairman Mary Schapiro said in a statement.

A report by the SEC's inspector general made public last week said that two agency lawyers, who were not identified, were under investigation by the FBI and federal prosecutors for possible criminal and civil violations related to insider trading. (Reporting by Martha Graybow)