The presidential campaign of Rep. Jack Kemp (R-N.Y.) has now borrowed more than $1 million but delayed the timing of the latest loan of roughly $500,000 to avoid having to report it publicly until next January.

The campaign, following Federal Election Commission rules, filed a quarterly report yesterday showing that it had borrowed $600,000. In fact, the campaign has run up loans in excess of $1 million.

The campaign purposely put off borrowing the additional cash until the first few days of October so that the new debt would not have to be disclosed in FEC reports covering the period from July 1 through Sept. 30.

The maneuver of delaying the loan to just after the reporting period is legal and functioned to prevent publicity about the extent to which the Kemp campaign is running into the red. In two separate interviews during the day, Kemp campaign spokesman John Buckley denied the existence of the additional borrowing.

Last night, however, Kemp personally acknowledged the additional loan. "We have borrowed it, it was authorized by me," Kemp said by phone from a Des Moines hotel.

Earlier in the day, Buckley said: "There has been none," when asked if any money over and above the publicly reported $600,000 had been borrowed.

Reached later in the evening at his home, Buckley qualified his answer to say: "To my knowledge, there is nothing to it," referring to questions about additional loans. He said that as a senior staff member he would know about such loans. "There has been no talk about further loans being taken out. That is the kind of information I would have known about . . . I'm being totally forthcoming to you."

When Kemp was reached in Des Moines, however, he acknowledged that a loan of about $500,000 had been taken out by the campaign. "Buckley didn't know," Kemp said, and was "embarrassed" when he later learned of the loan.

The money has been borrowed from the Sovran Bank/D.C. National using as collateral the money the Kemp campaign expects to receive in federal matching funds on Jan. 1, 1988. The total loan against the matching money is now just over $1.1 million.

Kemp said the money has been borrowed to finance costly direct mail fund-raising. He said his campaign has qualified for $2.5 million in matching funds and expects to qualify for $4 million by the end of this year. He said he had calculated all along that the campaign would have to borrow about $1 million against the matching money.

According to a preliminary examination of Kemp's report, total borrowing against the matching funds is roughly $1.1 million, and about $281,000 more is owed to vendors for a total debt of $1.38 million. The campaign reported having $407,165 cash on hand as of Sept. 30, indicating that it is in the red by a net amount of just under $1 million.

Kemp's campaign is clearly in far tougher financial shape than the campaigns of either Vice President Bush or Sen. Robert J. Dole (R-Kan.). Dole reported debts of $495,451 and cash on hand of $2.2 million. Bush reported debts of $325,644 and cash on hand of $4.8 million. Marion G. (Pat) Robertson reported that his campaign is in the red by $374,000, with debts of $637,141 and cash on hand of $263,000.

Buckley said late last night that "I wasn't lying to you" when he provided the initial assertions about the loan.