New calculations by the Agriculture Department have increased the projected cost of a pending Senate farm bill by at least $5 billion and heightened the chances of a presidential veto, Secretary John R. Block said yesterday.

Block said that a bumper harvest of most major crops and continuing decline of U.S. farm exports mean that the bill, expected to be on the Senate floor next week, could cost $60 billion to $70 billion over the next three years.

The congressional budget resolution set a three-year $34.8 billion spending limit on the measure, but USDA estimates based on July crop and market data put the cost at around $55 billion -- or $20 billion over budget. A House-passed farm bill is close to the $35 billion mark.

Block said that he and allies are heavily lobbying individual senators in an effort to persuade them to support floor amendments that would reduce the cost of the bill and meet other administration policy objections.

"I am deeply concerned about the cost of the bill, and Congress does not seem to be addressing the cost concerns that we all must have," he said. "It is time we came to our senses. This is just getting out of hand."

Block would not flatly predict a veto, but said "the bill is at risk, given the projected cost . . . . How can the president sign a bill that is this much over budget and at the same time promote deficit reductions? I don't think he can."

He conceded, however, that it seems unlikely that Congress will produce a final version that meets budget limits. "Practical politics tell us that we won't get all the money cut out . . . but we need to get it down as far as we can," he said.

On other matters, Block told reporters:

*The lower price-support loan rates on grain, rice and cotton that now seem likely in a final bill and new conservation programs are "major" changes in agricultural policy that he and the administration applaud.

*A dairy "diversion" plan in the House bill, which would pay farmers not to produce milk, is unacceptable to President Reagan and will be vetoed if it is in the final legislation.

*The administration also strongly objects to a Senate provision that would allow wheat farmers to vote on mandatory production controls.

*The department has drawn up no plans for dealing with the massive surpluses of grain and cotton that are expected to end up in government hands this year because of farmers' forfeiture of crop loans. More than 3 billion bushels of corn and wheat, on which farmers have received loans, are expected to be turned over.

Block said he "would not rule out" using some of the surplus in broadened foreign aid programs or using some as partial payments to farmers who enroll erodible land in the new conservation reserve created by the legislation.