"There should be no reason to believe that our peacekeeping operations will be underfunded," Miroslav Lajcak told reporters in Geneva.
Under pressure from the United States, UN member-states agreed in June to trim $600m from the previous peacekeeping budget of $7.87bn.
In a confidential report seen by AFP last week, Secretary General Antonio Guterres delivered a warning about the impact of peacekeeping cuts in the Democratic Republic of Congo, the UN's largest and most expensive mission.
He said the cost-cutting could cripple the 18 000-strong DRC peacekeeping force in its efforts to prevent a collapse of the vast, mineral-rich African country.
But Lajcak, a Slovakian diplomat who is presiding over the 72nd General Assembly session, sought to downplay those concerns.
"We will be able to make up for the [cuts] which have been announced", he said.
"They will not be that significant and there are member states who have already announced their readiness to cover" any gaps that emerge, he added.
The United States had sought a nearly $1bn cut in peacekeeping funding, as part of President Donald Trump's vow to crack down on UN waste.