The Senate sided with the administration yesterday in opposing restrictions on contributions to international lending institutions as it began voting on the annual foreign aid appropriation bill.

For the third year in a row the House has approved a series of amendments denying U.S. aid "directly or indirectly" to Vietnam, Cuba and several other nations unpopular here.

The World Bank and other international lending institutions said that if this language remained in the bill and became law they could not accept any U.S. contributions because they are forbidden to accept money that carries restrictions on its use.

In each of the last two years the Senate deleted these provisions from the aid bill and prevailed on the House to drop them. In a series of roll calls yesterday, the Senate by margins of 17 to 20 votes again deleted restrictions aimed at Vietnam, Cambodia and the Central African Empire (now Republic).

The Senate did vote 76 to 20 to approve a House provision barring aid "directly or indirectly" to Cuba, but by a later vote of 50 to 44 struck out the words "or indirectly." This had the effect of exempting U.S. contributions to the World Bank from any restrictions. To leave in the word "indirectly" could lead to the death of the World Bank, aid advocates said.

By a vote of 58 to 39, the Senate upheld House language barring direct aid to Mozambique, but the president could waive the prohibition in the national interest.

Sen. Daniel Inouye (D-Hawaii), floor manager of the bill, pleaded with the Senate in each case to delete the restrictions so as not to tie the president's hands in the conduct of foreign policy.

The bill before the Senate provides $8.4 billion in foreign aid for the year that began Oct. 1. The administration had asked for $9.3 billion and the House voted $7.7 billion.

On the other side of the Capitol, the House passed and sent to the Senate bills that would:

Extend to June 1, 1981, the prohibition against the issuing of Internal Revenue Service regulations taxing employes' fringe benefits as income.

Authorize $20.8 million for participation in an international energy exposition in Knoxville, Tenn., in 1982.

Write into law changes the House has made in its rules to tighten restrictions on use of the congressional frank. One provision would forbid a member of Congress to mail free congratulations to a constituent for some act of "personal distinction," though the frank could be used to laud "public distinction." Rep. Samuel Stratton (D-N.Y.) complained that managers of the bill could not explain the difference.