Responding to mounting eveidence that hundreds of millions of dollars worth of coal may have been poached from federal lands in the East, the government is trying to retrieve $2.7 million from an Atlanta-based company accused of illegal mining.

The U.S. Bureau of Land Management, in an internal staff report prepared last year, has estimated that, based on surspected cases of illegal nining in four Alabama counties. coal worth between $135 million and $1 billion may have been taken illegally out of East Coast federal reserves over the years.

Officials concede the estimates are rough, based on "guesses" as well as projections, and say they may not know the extent of illegal mining for some time.

What they have found so far is roughly 30 cases of suspected "trespass" on roughly 1,100 of 70,500 acres of federal coal reserves in Alabama. Investigations are currently underway in four Alabama counties: Fayette, Walker, Jefferson and Tuscaloosa.

In once case, officials said, the Bureau has ordered Invesco International Corp. of Atlanta to pay $2.7 million for allegedly taking more than 150,000 tons of coal from government-owned reserves on land adjacent to its stripmining operations in Fayette County, Ala.

Government officials said Invesco has told them than any mining of federal coal was inadvertent. They said, however,that the government has not ruled our a willful violation, which could result in a higher assessment.

Attempts to reach Invesco executives yesterday were unsuccessful, but Coal Week, a McGraw-Hill trade publication, quoted company officials as saying that, at most, 40,000 tons had been removed, all accidentally.

Officials of the Bureau, an agency of the Interior Department, said socalled "trespass," or illegal use of federal lands or reserves, is a pervasive problem and one that was overlooked in the East for years because of government preoccupation with Western reserves.

But, with renewed interest in coal, especially Eastern coal, the Bureau opened a field office in Tuscaloosa in May 1977, prompting a citizen complaint that led to the Invesco case and about 30 others in the four-county area.

Officials said any illegal activity in the 30 mining operations has been halted. Some suspected violations, they said, go back a number of years. In the case of Invesco, the alleged violation occured in August, 1977.