The call came in the morning to the lawyer representing Manuel Guerra, an illegal immigrant from Mexico living in Florida who had been caught in a tortuous and seemingly failing five-year court fight against deportation.

With the news early Thursday that federal immigration authorities had canceled his deportation, Mr. Guerra became one of the first illegal immigrants in the country to see results from a policy the Obama administration unveiled in Washington that day. It could lead to the suspension in coming months of deportation proceedings against tens of thousands of immigrants.

A working group from the Homeland Security and Justice Departments met Friday to initiate a review of about 300,000 deportation cases currently before the immigration courts. Under the policy, immigration authorities will use powers of prosecutorial discretion in existing law to suspend the deportations of most immigrants who, although they have committed immigration violations (which generally are civil offenses), have not been convicted of crimes