WASHINGTON (AP) _ Selected post offices around the country are closed today as a result of cuts in the federal budget.

Postmaster General Preston R. Tisch said earlier this week that budget legislation calling for a $1.25 billion reduction in postal spending would cause cancellation of three-fourths of the Postal Service's 1988 construction projects.

Tisch also said selected offices would be closed today and next Saturday, Jan. 2. The Saturday post office closings were being announced locally, he said.

Division managers decided which offices were to be closed.

Even when local offices were closed, Saturday deliveries were not canceled. Such a move would have required permission from Congress.

Tisch said that in response to the budget cuts, the agency would cancel 50 percent of the construction projects planned for the next two years, including some 75 percent of those scheduled for 1988.

''The net effect of this will be that new facility construction projects not already under contract will be eliminated,'' Tisch said in a statement Wednesday.

Postal officials said managers were reviewing a list of several hundred construction projects to determine where cuts would be made, and that the decisions would be announced locally.

Tisch also said transportation for some third- and fourth-class mail would be consolidated, a step which should save money but could slow these classes of mail by a day or two. Third class mail is generally advertising materials while fourth class is parcels.

Cuts also will be made in planned purchases of new equipment and vehicles, Tisch said.