The consortium that hopes to build the $20 billion Alaskan natural gas pipeline and three oil companies with most of the Prudhoe Bay gas agreed yesterday to come up with a plan by mid-April for completing final engineering details and cost estimates.

At a two-hour meeting with Energy Secretary Charles Duncan and his deputy, John Sawhill, the two sides also said that by the same date they would outline formally their areas of agreement and disagreement on construction, ownership and operation of the pipeline. They also will set a timetable for resolving their differences.

It was the two sides' first face-to-face meeting since Northwest Alaskan Pipeline Co., a partnership of several gas pipeline companies, was picked by the government in 1977 to build the new line.

Under current law, the oil companies are barred from having an ownership or management role in the finished pipeline. The pipeline consortium, however, doesn't have the financial resources to build the line without help from the oil companies or some form of government loan guarantees.

Duncan and the administration are trying to avoid having the federal government assume any financial role in the pipeline. Bringing in the oil companies, on the other hand, probably would require new legislation.

Sources said yesterday's meeting was "harmonious" after Duncan led off with a pointed statement that he expected the two sides to make progress at the meeting. "The American people have a right to expect progress . . . on this vital program," he declared.

Attending the session were officials from Exxon U.S.A., Arco and Sohio, along with John McMillan, head of Northwest Alaskan, and Gov. Jay Hammond of Alaska.

The final engineering studies and cost estimates will cost about $500 million, and one of the major issues has been whether the oil companies would agree to finance part of that prior to an understanding about their ultimate role in the pipeline.

Meanwhile, the project's schedule keeps slipping while the struggle over financing continues. Field work for this summer has been delayed, and congressional sources doubt there will be time this year to pass any amendments to the 1977 legislation that would allow the oil companies a larger role.

"If we wanted to legislate this Congress, I don't know if we could," said one Senate energy expert.

The delays have added substantially to the project's cost, as well. At the same time, the value of the 26 trillion cubic feet of gas at Prudhoe Bay has risen even faster. As the Senate energy specialist put it, "The economics of the project have done nothing but improve since it was announced."

The completed pipeline system, with two legs in Canada taking gas to the western and midwestern states, would carry about 2.4 billion cubic feet a day, about 5 percent of U.S. consumption.