Hopes of another international peace conference on Syria before the end of July are fading, the U.N.'s special representative for the war-torn country said Tuesday.

On his way into daylong talks between the U.S. and Russia, Lakhdar Brahimi told reporters he still hopes a second round of international negotiations to find a political solution to the conflict can be convened in Geneva — but not until later in the summer.

"Frankly now, I doubt whether the conference will take place in July," he said, noting that the Syrian opposition is not meeting until early July and probably would not be ready. "Since our previous meeting here on the 5th of June, the situation on the ground in Syria has hardly improved. It is still relentless destruction, killing, more suffering, more injustice, and more uncertainty for the future of the Syrian people."