As the Mexican economy deteriorated in the past several months, the number of illegal aliens arrested along the U.S. border with Mexico jumped dramatically, according to Commissioner Alan C. Nelson of the Immigration and Naturalization Service.

Nelson said yesterday that arrests along the southern border for the last three months of 1982 were up about 20 percent, putting them at an all-time high. But in the first half of January the number of arrests was running at an average about 50 percent higher than last year.

If the present trend continues, Nelson said the Border Patrol could arrest nearly 1 million people this year. The only other time the numbers have gone nearly that high was in 1954, when the government carried out Operation Wetback and conducted roundups of illegal immigrants.

The Border Patrol arrested 819,919 illegal aliens in 1982.

"No one can say for certain the reasons for this unprecedented flow of people illegally crossing our southern border," Nelson said. "However, the recent peso devaluation in Mexico and reported economic difficulty in that country likely are contributing factors."

Nelson said there are aliens other than Mexicans streaming across the southern border, including a significant number of people from El Salvador, but he had no breakdown on their nationalities. He also had no estimate on how many aliens successfully cross the border for each one apprehended.

He said the problem is especially severe at the Chula Vista, Calif., border section between San Diego and Tijuana, Mexico, where the number of arrests has jumped 74 percent over the number in the first half of January, 1982. As a result, Nelson has ordered 60 additional Border Patrol agents to assist temporarily the 470 already at Chula Vista.