A core group of member states will meet to examine a revised draft of the document that will be submitted to world leaders at their three day summit opening on Wednesday.
Other delegations spoke of slow but steady progress overall.
After marathon overnight talks on seven contentious issues, a US spokesman said the discussions on setting up a revamped human rights council and on UN management reforms had fallen apart.
“These two issues, management and human rights council, have currently collapsed,” the spokesman, Rick Grenell, told reporters as the core group raced against the clock to finalise a draft document for the summit.
Adding to the tensions, UN secretary general Kofi Annan put off a press conference scheduled for Monday for 24 hours.
The core group ground on with efforts to nail down a deal on development, terrorism, human rights, responsibility to protect peoples threatened with genocide, disarmament and non-proliferation, UN management reform and setting up a peace-building commission.
Some countries object to two key criteria set for creation of the revamped UN human rights council to replace the current, discredited Human Rights Commission.
“Certain countries have decided that the two-third majority vote of the General Assembly criteria to get on the human rights council is not acceptable, that a simple majority should be the rule. … That’s troubling to us,” Mr Grenell said.
Brazil’s UN envoy Ronaldo Sardenberg denied that the talks on human rights had fallen apart.
He said Britain had submitted a compromise text that “accepts the idea of (a human rights council) in principle and then sends it to the General Assembly to study the modalities.”
Currently, members of the Geneva-based rights commission are elected within UN regional groups.
“If the Human Rights Commission is going to remain exactly the same with the violators in control, we have a problem,” Mr Grenell said.
Those countries were also objecting to the new council sitting as a permanent body of the UN, he said.
A US official, who asked not to be named, identified the countries which raised the objections as Egypt, China, Russia and Pakistan.
The proposal on the table was for a standing meeting of the human rights council throughout the year, instead of the annual six-week session that the Geneva commission holds.
“On management (reform), we also have fallen apart,” Mr Grenell said.
“It’s a very coordinated effort by the non-aligned movement,” he added.
“The leaders of the non-aligned movement have stood against different aspects of management reform.”
“What we would like to see is more powers given to the Secretary General, hold him accountable, give him the ability to prioritize mandates, prioritize personnel and then hold him accountable,” Grenell said.
“We cannot have the General Assembly continue to operate with business as usual.”
UN spokesman Stephane Dujarric told a press briefing that progress was made in intensive weekend talks on development, terrorism and UN management reform.
Member states were still far apart in other areas, particularly on disarmament and non-proliferation, he added.
Mr Dujarric said Jean Ping, the Gabonese official who is current head of the General Assembly and steering the crisis talks on the reform package, would submit a revised version of the summit document to member states later Monday.