U.N.Ambassador Andrew Young said today that a "continuing relationship with the Mexican government is necessary to work out the problem" of illegal aliens in the United States, most of whom are Mexican.

After a day of talks with Mexican President Jose Lopez Portillo on aliens and other issues, Young said the illegal migrant problem cannot "be solved by one single act of Congress."

He referred to President Carter's plan sent to Congress last week, to legalize the status of 4 million to 12 million illegal aliens. The plan would give full residence to illegals who entered the United States before 1970. The rest would receive five year work permits if they register with U.S. authorities.

Young called the presidential plan "one big step in the overall process of resolving the problem."

He spoke at an airport news conference shortly before leaving for Costa Rica to meet President Daniel Oduber, his third stop on a 10 nation tour of Caribbean countries.

U.S. source said Young had turned down an invitation to met with Cuban officials during his tour.

Cuban U.N envoys noted that Young would be "45 minutes from Havana" during a stop in Jamaica's Prime Minister Michael N. Manley, a close friend of Fidel Castro, would be able to arrange a meeting.

But Young apparently devided such a get-together did not fit into his trip which is aimed at strengtening ties with America's traditional friends.

Many illegal aliens cross the U.S. border from Mexico in search of better-paying jobs. That migration had increased sharply in the past two years as a result of a slump in the Mexican economy.

The ambassador quoted Lopex Portillo as saying "Mexico will never really be satisfied until it exports commodities and goods to the United States and no people." Young said he looks forward to that day as well.

Mexican officials want more trade concessions from the United States to help boast at the Mexican economy and created more jobs which they say would relieve the pressure on Mexicans to emigrate.

Young also spoke of a provision in Carter's proposed law tht would make it a civil offense for an employer to hire an illegal alien knowingly. The offense would be punishable by a $1,000 fine for each alien hired. Illegal migrants have complained that employers, who hired them to do farm labor generally shunned by Americans, underpay and abuse them and threaten deportation if they complain.

"Once the illegal aliens are not fearful of deportation, they will have the right to organize and they will be able to bargain collectively and be protected by American laws," Young said.

Asked if a Mexican U.S. treaty is necessary to protect the rights of Mexican migrants, he said American law is sufficient.

Young described his Mexican stop as "very imformative and a very productive visit."

He said he covered "an amazing amount of material" in his talks with Lopez Portillo and Foreign minister Santiago Roel Carcia, including "attempts to reach a satisfactory treaty on the Panama Canal."