President Reagan, warning that the situation in Central America "is not a crisis we can afford to ignore," formally asked Congress yesterday to approve the funds and legislation necessary to implement his Caribbean Basin initiative to attack poverty and unrest in the region.

At a ceremony in the White House Roosevelt Room, which contains a portrait of Theodore Roosevelt in the Rough Rider uniform he wore in Cuba, Reagan signed the message sending to Congress a thick package of legislative proposals designed to counter alleged efforts by the present-day Cuban government of President Fidel Castro to extend communist influence in this hemisphere.

The administration hopes to do this through a combination of measures including $350 million in emergency economic assistance, a 12-year period of duty-free entry to this country for virtually all Caribbean exports and a variety of tax incentives to encourage U.S. private investment in the region.

"This is of vital interest to us in our own front yard," the president said. "If we don't act now, the dangers will grow . . .new Cubas will arise."

But, while Reagan asserted that the program was "not a partisan issue" and appealed to Congress not to make major changes or cuts, the first replies from Capitol Hill indicated that at least one part of the package--the tax incentives for investors willing to build factories in the region--faces potentially serious opposition from legislators fearful it will cause a loss of jobs in this country.

Although the Caribbean initiative was unveiled with great fanfare in a speech by Reagan last month, lately it has become an almost forgotten part of the administration's policy toward the region. Instead, during recent days most public attention has been focused on other aspects of the president's policy, such as military aid to El Salvador and the rising tensions over Nicaragua's alleged aid to the Salvadoran guerrillas.

Yesterday, the president tried to shift attention back to the Caribbean initiative by giving it another rhetorical sendoff on its way to Congress and by sending Thomas O. Enders, assistant secretary of state for inter-American affairs, and William E. Brock, the U.S. special trade representative, to open the first round of congressional hearings on the subject.

Both immediately found that, despite controversy over the administration's approach to El Salvador, most of the program appears to have strong congressional support. But, it also became clear, that support does not extend to the part of the plan that proposes extending to prospective investors in the region the same preferential tax treatment for fixed-asset expenditures available in the United States under the domestic investment tax credit.

Enders, who appeared before a Senate Appropriations subcommittee, was told by Warren B. Rudman (R-N.H.) and J. Bennett Johnston (D-La.) that they feared it would lead to a flight of jobs from the United States, Puerto Rico and the Virgin Islands. Rudman said: "I oppose it, and I will try to build up support to vote against it."

Brock, testifying before the House Ways and Means Committee, heard the same concern from members representing states with high unemployment, such as Pennsylvania and Ohio. Typical was the comment of Rep. Don Bailey (D-Pa.), who asked: "How do I go to an American worker, losing a job, and justifying nothing more than exporting technology and capital by this mechanism?"

Enders also encountered pointed questioning about what the United States will do if the scheduled March 28 elections in El Salvador give the lead in shaping a future government to the extreme right. He replied that the administration intends to support a government "headed in a fundamental reforming way that is the basis for U.S. policy" and added that this requires respect for human rights, democratic institutions, a free labor movement and subordination of the military to civilian authority.

Of the additional $350 million in economic aid being sought by the administration, $128 million is earmarked for El Salvador. Other requests include $70 million for Costa Rica, $50 million for Jamaica, $40 million for the Dominican Republic, $35 million for Honduras, $10 million for Belize, $5 million for Haiti, $10 million for the Caribbean ministate islands and $2 million for regional labor development programs.