President Carter late yesterday signed an executive order that authorizes a $2.9 billion raise, effective this month, for the government's 1 million-plus white-collar workers.

Federal payroll offices had been awaiting the action so they could put the 9.1 percent increase into effect. Final wording of the order, which was sent to the president while he was abroad Air Force One, had been delayed while government attorneys wrestled over a legal question involving raises of about $900 a year for some 700 top career officials. Payroll offices have until today to get the raises into the next payroll checks.

Carter authorized the increase last August to be effective with the first October pay period.

In addition to the possible extra raise for a handful of workers in Grade 16, and about 619 lower-level members of the Senior Executive Service, the new pay charts that federal agencies will issue to go along with the executive order also will reflect slightly higher amounts due some workers in various longevity steps to pay grades GS1 and 2.

Government payroll offices have been nervous because the EO had not been signed, and the time for them to compute new salary schedules -- and put them into pay checks -- was drawing near. The 9.1 percent raise for employes making $50,112.50 and under will be effective with the first pay period beginning after Oct. 1. For most government employes, that new pay period, with the higher salaries, began Oct. 5.

The legal hangup came when government lawyers questioned whether the first step for Grade 16 personnel (there are only about 85 of them government-wide) should be $49,198, as the pay charts released by the government indicated, or whether those employes should be allowed to float to the career salary maximum of $50,112.50. Although it sounds like small potatoes when a $2.9 billion raise is involved, lawyers argued that important precedents could be set that would affect future raises for super-grade level employes.

Federal officials already have agreed that the pay chart issued when the president announced the 9.1 percent raise (that chart was carried here in late August) had several errors at Grades 1 and 2. They will be corrected as follows: The new rates will reflect higher pay levels for employes in steps six, seven, eight and nine in Grade 1, and higher levels for steps three and four of Grade 2.When the average 9.1 percent raise goes into effect, the average salary of federal white-collar workers will jump to $21,680. Because this is a headquarters town, with more personnel in higher-grade posts, the average salary for the 300,000 white-collar federal workers here will be around $23,000 a year.