By ZEINA KARAM 01/28/14 05:29 AM ET EST

GENEVA (AP) — The key issue of a transitional government to replace President Bashar Assad blocked any progress Monday in Syrian peace talks, described by one delegate as “a dialogue of the deaf.”

The chief U.N. mediator expressed frustration over inflammatory public remarks by the two sides as he sought to identify some less-contentious issues in hopes of achieving any progress at all at the bargaining table.

But even the most modest attempts at confidence-building measures faltered — including humanitarian aid convoys to besieged parts of the central city of Homs and the release of detainees. Veteran mediator Lakhdar Brahimi somberly declared at the end of the day that he had little to report.

“There are no miracles here,” Brahimi said, adding that both sides nevertheless appeared to have the will to continue the discussions. Asked how he planned to bridge the enormous gap between the two sides, the veteran diplomat quipped: “Ideas, I’ll take them with great pleasure.”

The gulf between the two sides was on full display at a turbulent morning session in which the delegations from the opposition and the Syrian government faced off on the question of Assad’s future.

The Western-backed Syrian National Coalition wants an interim replacement for Assad, reiterating at every opportunity that the stated goal of the peace conference, agreed upon by international powers in preliminary talks in June, is to establish a transitional government with full executive powers.

But Assad, whose troops have a tenuous upper hand in Syria, has said he has no intention of stepping down and, on the contrary, may run again for president later this year. His delegates have capitalized on the ascendance of Islamic militants, saying the priority at the peace conference was to finds ways to combat terrorism.

“We came here with the intention of discussing a transitional governing body and they came with the intention of consecrating Bashar Assad’s presence,” said Rima Fleihan, a member of the coalition’s negotiating team.

Murhaf Jouejati of the coalition said the meeting ended on a “sour note,” and the session was broken up by Brahimi after the government delegation became confrontational.

Syria’s uprising began in March 2011 with largely peaceful protests that eventually turned into an insurgency and full blown civil war after a harsh military crackdown. The war has become a proxy conflict between regional powerhouses Iran and Saudi Arabia, with hints of a throwback to the Cold War as Russia and the United States back opposite sides.

Despite the rancorous rhetoric outside the conference room, both sides have said they won’t withdraw from the talks.

Brahimi said the parties were talking to the media “too much,” adding that he asked them to respect the confidentiality of the discussions and avoid exaggerations. Still, all signs pointed to impasse.

White House spokesman Jay Carney said the U.S. was “realistic about how difficult this is going to be, but we are completely convinced that this is the only way forward for Syria, and that’s through negotiations.”

“What’s important is that the two parties have sat in the same room over the past several days to discuss critical issues. And this process is ongoing. And I would expect quite a few ups and downs along the way,” Carney said. “But it is the only way to end the conflict in Syria. It has to be ended through a negotiated political settlement.”

On Sunday, after three days of talks, a tentative agreement was reached for the evacuation of women and children trapped in Homs before aid convoys go in. As of Monday night, there was no progress on the ground.

Brahimi cited security problems for part of the delay. The opposition delegation has little control over armed groups inside Syria. Fighters affiliated with the Western-backed coalition have been engaged in deadly fighting with al-Qaida-backed militants, who do not accept the coalition’s authority and do not feel bound by agreements reached in Geneva.

The most powerful rebel groups include two that the U.S. has formally designated as foreign terrorist organizations: the Iraqi State of Iraq and the Levant, and Jabhat al-Nusra.

On Monday, talks were supposed to shift to thorny political issues such as Assad’s future.

As the meeting got underway, the government delegation put forward a paper focusing on the need to combat terrorism and halt funding and shipments of weapons to rebels fighting to topple Assad, delegates said.

Bouthaina Shaaban, an Assad adviser, called the paper an “expression of good will” in search of common ground, and said she was surprised the opposition rejected it.

“Either these people have no capacity to express their love and care for Syria, or they are ordered by foreign powers to ignore what is most important and most urgent for their country,” she said.

The opposition called the paper a deviation from the talks’ main goal of a transitional government.

The Britain-based Syrian Observatory for Human Rights, which tracks the fighting, estimated that 1,200 women, children and elderly people are trapped in besieged areas of the old quarter of Homs.

The opposition accused authorities of blocking a convoy of 12 trucks trying to get into the embattled city and said, “We will judge the regime by what it does, not by what it says.”

Shaaban dismissed the aid effort for Homs as a distraction aimed at bolstering the opposition’s credentials.

“This is to make a big fuss about taking two trollies to Homs,” she said. “Is this why we came to Geneva? Or we came here to solve the problem in Syria?” she said.

Homs Governor Talal Barrazi said the only obstacle to the flow of food into rebel-held areas was “some cases of sniper fire by terrorist groups.”

In a statement released by his office, Barrazi said it is willing to evacuate civilians who want to leave the old quarter to “any place they want to go to,” and they will get food and medical supplies.

“We are waiting for an answer from international organization representatives to specify the number of those who want to leave,” Barrazi said.

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Associated Press writers John Heilprin in Geneva, Bassem Mroue in Beirut and Albert Aji in Damascus, as well as White House Correspondent Julie Pace, contributed to this report.