President Reagan yesterday called for an end to barriers against the free flow of international investment, claiming it was "a vital and necessary ingredient in a stable, growing world economy."

In a statement issued by the White House, Reagan deplored growing trends in other nations that restrict foreign investments and said the United States supports the concept of equal treatment for overseas and domestic investors. He added that the United States will seek treaties with individual nations to open investment flows and use already existing agreements to make sure American investors are not being discriminated against.

"As the predominate home and host country for foreign direct investment," the president said, "we have a substantial interest in the conditions under which these flows occur."

The United States in recent years has been a haven for overseas investors to the point that as recently as 1977 many Americans feared foreign takeovers of key industries and farmland. Lured by high interest rates in this country, foreign investment in the U.S. reached its peak of close to $22 billion in 1981 then, because of the global recession, dropped to $10 billion last year.

The Reagan administration has welcomed foreign capital inflow as a way to cover high government deficits without taking funds from the private capital markets needed for industrial investments.

"I frankly would like to see a lot more invested here," U.S. Trade Representative William E. Brock said at a briefing on the president's statement.

Reagan's White House statement accompanied a Miami speech by Treasury Secretary Donald T. Regan in which he told the Hemispheric Congress of Latin Chambers of Commerce, "Foreign investment flows which respond to private market forces will lead to a more efficient international production and thereby benefit both home and host countries."

"In our opinion," the treasury secretary continued, "a free and open international investment climate will play a key role, not only in sustaining our own recovery here at home, but also in resolving many of the current international debt problems."

Regan challenged the capital-poor Latin nations that include the world's two largest debtor nations--Brazil and Mexico--on their investment flow policies, asking, "Is the influx of foreign capital welcomed or is it feared?

"For our part," he continued, "we would like to invest in your economy and we would like you to invest in ours. We share a common future."

Many Latin nations, however, remember U.S. domination of their economies and fear American investment. Moreover, they believe their citizens' dollars are needed more at home than in the United States and are concerned that a drain of hard currency for investment in America, as Regan suggested, will impede their chances for industrial development.