Citicorp, the world's largest bank holding company, reported yesterday that second-quarter earnings rose 22 percent, while Manufacturers Hanover Corp. said earnings rose 33.6 percent.

Lower interest rates helped them post big increases from securities trading and management of their investment portfolios. But these gains were partially offset by bigger provisions for possible loan losses.

Meanwhile, two firms recently involved in a merger fight reported earnings yesterday. Baxter Travenol Laboratories Inc. said second-quarter profit fell 8 percent, while Hospital Corp. of America, reported a 25 percent gain. Also yesterday, GTE Corp. said its profits were up 0.7 percent.

Citicorp, with $1.2 billion of its $159.6 billion total assets in loans to Argentina, said it did not exclude its share of $570 million in overdue Argentine public-sector interest payments from earnings because they "were not material in amount." Roughly half of Citi's exposure is in the private sector.

MHT, whose principal subsidiary, Manufacturers Hanover Trust, is the largest U.S. lender to Argentina, with $1.3 billion, added its $26.3 million share of the overdue interest payments to earnings, but put an additional amount in loan loss reserves to neutralize the impact.

MHT said $59.5 million of Argentine payments remain past due.

Despite this, and a doubling of provision for loan losses to $161.3 million in the quarter, MHT earned $98.5 million ($1.97), up from $73.7 million ($1.41) last year.

Citicorp earned $251 million ($1.81) in the second quarter, up from $206 million ($1.48) in the same period of 1984.

* Baxter Travenol Laboratories Inc., a medical supplier which has agreed to a $3.8 billion merger with American Hospital Supply Corp., reported yesterday that its second-quarter profit fell 8 percent despite a 6 percent sales gain.

Meanwhile, Hospital Corp. of America, one of the world's largest health-care companies, posted a 25 percent profit increase on a 16 percent sales gain in the second quarter.

Monday's merger agreement between American Hospital and Baxter voided American's earlier plans to merge with HCA.

* GTE Corp. said yesterday that its profit edged up 0.7 percent in the second quarter as gains from its basic telephone service were offset by an operating loss at its GTE Sprint long-distance service.

GTE, based in Stamford, Cn., said its 2nd quarter profit rose to $285 million from $283 million a year earlier.