President Reagan today saluted the members of Congress who voted to build the MX missile last month, saying that they are protecting America's independence with a show of "political courage."

In a radio speech filled with references to the Fourth of July, the president said that courage is required not only in revolutions and wars but in politics.

"It was not easy for many of these men and women to vote for the MX missile," Reagan said. "Some have been harshly criticized by others members in their own party. Indeed, they face considerable pressure and corresponding political risks. While accepting such risks, the only benefit they've received is the knowledge that they place foremost their hopes for successful arms reduction and greater security of their nation."

It was Reagan's second statement in two days on the arms race, manifesting a renewed effort by the president to build support for his proposed increases in the defense budget, his tough bargaining stance in arms talks with the Soviet Union and his Latin American policies.

On Friday, in a statement on the 15th anniversary of the treaty on the nonproliferation of nuclear weapons, Reagan said he is committed to achieving "real, substantive progress towards an agreement involving significant reductions in U.S. and Soviet strategic nuclear arsenals to more equal, more stable levels."

Administration officials said that the president feels he must reemphasize the need for American military strength if he is to win public support.

This weekend Reagan is planning to attend a party celebrating his wife's 60th birthday.