Deadlock after a week of Hong Kong protests.

Hong Kong (CNN) -- A week into paralyzing pro-democracy protests in Hong Kong, authorities and demonstrators are still at loggerheads.

Both sides say they are open to talks, but each wants concessions from the other.

A student group said Sunday that it would restart dialogue with the government if police do a better job of handling clashes between pro-democracy protesters and people opposed to the demonstrations.

The protesters, many of them students, have blocked major highways in several key districts for the past week, challenging a decision by Beijing about how elections will work in the semi autonomous Chinese territory.

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Hong Kong's top leader, Chief Executive C.Y. Leung, has called on the demonstrators to disperse by Monday so that classes can resume at schools and government employees can go back to work at offices surrounded by protesters.

Some demonstrators said Sunday that they'd make a major concession, but other protesters prevented it from going through.

Demonstrators were withdrawing from outside the chief executive's office, a key point of tension with authorities, the protest group Occupy Central with Love and Peace said on its Twitter account.

The group also said that demonstrators at the Mong Kok protest site, where clashes have taken place with opponents of the movement, would relocate to the main protest site on a multilane highway near the government headquarters.

But other protesters did not want to comply with Occupancy's announcement. They sat on the ground, and barricades were not moved.

Afterward, Occupy sent out another tweet, saying protesters had returned to the sites they had intended to clear.

Clashes in busy area

Dozens of people were injured as scuffles broke out Friday and Saturday at the protest site in Mong Kok, a tightly packed district of shops and residences surrounding one of the city's busiest intersections.

Students and other protesters have accused police of failing to protect them from attacks by people who want an end to the demonstrations.

Police have rejected the accusations, calling them "totally unfounded and extremely unfair to police officers who faithfully and diligently performed their duty at the scene."

At least 30 people have been arrested since Friday, police said, adding that at least eight were believed to have links to organized crime groups, known as triads.

Access to government building in dispute

The protesters broke off planned talks with Leung's second-in-command, Chief Secretary Carrie Lam, because of the violence.

"The precondition for opening the dialogue between students and the government is that police should properly handle the clashes between pro-occupation protesters and opposing citizens," the Hong Kong Federation of Students said in a statement Sunday.

"If the second point is confirmed, students are willing to re-open dialogue with the government right away," the statement said.

The students disputed the government's assertion that government workers can't access the headquarters.

"The passage to the government headquarters has always been kept open, the 3000 civil servants can enter into the building," the student federation said. "The Administration's Office can ask the employees to return to their workplace, the government should not continue to confuse and mislead people."

The government issued its own statement saying "the door to dialogue is always open" if the students are willing.

It also said it hoped the protesters would open up a footbridge and several roads around the government building.

University official urges protesters to leave

A senior official at one of the city's top universities called on students to leave the protest areas immediately, saying he feared for their well-being.

"I am making this appeal from my heart because I genuinely believe that if you stay, there is a risk to your safety," Peter Mathieson, president and vice-chancellor of Hong Kong University, said in a message to students early Sunday. "Please leave now: you owe it to your loved ones to put your safety above all other considerations."

Demonstrators are upset with a decision this summer by China's ruling Communist Party to let a committee stacked with Beijing loyalists choose who can run as a candidate for the chief executive role in the 2017 election.

A new electoral system will, for the first time, let the city's 5 million eligible voters pick a winner rather than the largely pro-Beijing committee of 1,200 members that has chosen past leaders. But critics argue that the right to vote is pointless if the candidates are handpicked by Beijing.

They complain the Chinese government is encroaching too heavily on the affairs of Hong Kong, which has been governed according to the "one country, two systems" policy since Britain handed it back to China in 1997.

Support for the protest swelled last Sunday, when police used tear gas and pepper spray in a failed effort to disperse demonstrators. The use of such heavy-handed tactics shocked many residents in Hong Kong, where protests usually unfold peacefully.

The Chinese and Hong Kong governments have declared the demonstrations illegal. Beijing has heavily restricted the flow of information on the Chinese mainland about the protest movement.

CNN's Anjali Tsui and translator Daisy Ng contributed to this report.