American Telephone & Telegraph Co. and the federal government finally came to one agreement last week in the Justice Department's landmark antitrust case against the communications giant.

Both said they wanted to speed the process of gathering information so a trial could start as quickly as possible.

There's only one hitch: Neither party yet agrees that the other's description of history and events in the communications business adds up to "the true facts."

In a hearing before U.S. District Court Judge Harold Greene, an AT&T lawyer suggested that, contrary to government allegations that the telephone company has been guilty of "foot-dragging," a quick trial is desired so that the alleged antitrust violations can be rebutted and "disproved."

In fact, AT&T said if the government would agree to a stipulation of "the basic facts relevant to the real issues in this case -- then the case could be speedily brought to trial," the company later recounted in an unusual press release.

"AT&T told the court that if the government would agree to these basic facts, then the discovery requirements could be sufficiently reduced for trial to begin by the end of this year," the press release stated.

Justice Department lawyer Kenneth Anderson, who heads the Antitrust Division's team in the four-year-old case, welcomed AT&T's statement as evidence that the company may have abandoned what he described as tactics that had delayed progress to date, including efforts -- so far futile -- to block government access to documents in private antitrust suits against AT&T.

But he cautioned that what AT&T is seeking to get the Justice Department to approve is "their view of the world." Rather, he suggested, the telephone company might just as well accept the government's presentation of "facts."

"If they are willing to stipulate our facts, we can go to trial in April," he added.

Under an expedited process already begun, a series of four exchanges of "contentions and proofs" in the case has started. AT&T issued its first major response to government charges on Jan. 8, arguing that the Justice Department was wrong in its allegations and contending that recent changes in telecommunications competition had made charges moot.

A second round of filings is due in April and May, and the series of charges and countercharges is due to end in April 1980. Justice is seeking to force AT&T to divest some of its diverse holdings -- such as its manufacturing arm, Western Electric Co.

The "basic facts" AT&T wants the government to accept relate mostly to the history of technology, structure, economics and regulation in the industry, the company stated. But Anderson said last night that AT&T has provided "little support for any of it" in documents filed to date.

Judge Greene is expected to advise the parties in the near future of his own view about possibly speeding proceedings by agreements on certain facts. But Anderson said he can't make any such agreement until AT&T turns over some remaining documents the Justice Department wants to study.