The war has killed more than 140,000 people and displaced millions since the unrest began in March 2011.
Brahimi briefed the UN Security Council Thursday on the conflict and the collapse in February of a second round of peace talks between the Syrian government and the opposition in Geneva.
Brahimi broke off the talks, known as Geneva II, to give the government and opposition an opportunity to take stock, and without setting a date for another round of negotiations.
"We would like the help of the Council and all those who can help to make sure that if and when we have a third round it will be a little bit more productive than the second one," he said.
Russia and the United States have been at odds for years over Syria and with both countries now at loggerheads over Ukraine, Western diplomats fear Moscow is in no mood to further pressure Damascus as they bet on a military victory for the Syrian regime.
Brahimi refused to be drawn by reporters Thursday on whether he had made a specific appeal to Russia.
He said he briefed the Council, of which Russia is a permanent member, on the situation and that it was "up to them to see if they can do something."
The three-hour session ended with the Council unable to agree on a joint press statement, said Luxembourg ambassador Sylvie Lucas, whose country holds the body's rotating presidency.
She said there had been "some discussion" about Brahimi's view that "plans to hold presidential elections in the coming months would be incompatible with the Geneva process".
Council members expressed "full support" for a resumption of talks in Geneva and in Brahimi's efforts, Lucas added.
Diplomats have said there cannot be a third round of peace talks unless both sides agree on the agenda and approach.
At Geneva II, Damascus insisted on prioritizing terrorism while the opposition wanted to put in place a transitional government that would strip Assad of all or part of his powers.