(CNN) -- As the total death toll in Syria climbed past 7,500, according to U.N. estimates, U.S. Secretary of State Hillary Clinton said Syrian President Bashar al-Assad could be tried for war crimes.
However, Clinton said Tuesday, pursuing charges against al-Assad might hinder efforts to persuade him to cede power.
The United Nations has credible reports that "the death toll now often exceeds 100 civilians a day, including women and children," Lynn Pascoe, a senior U.N. official, told the Security Council. "The total is certainly well over 7,500."
Tunisia, meanwhile, has offered al-Assad asylum if he steps down, its state news agency reported.
The number Pascoe cited is still below the 9,000-plus that opposition activists say have died in the nearly year-long attempt to put down opposition to al-Assad. At least 104 people, including three women and two children, were killed across Syria on Tuesday alone, said the Local Coordination Committees of Syria, a network of opposition activists.
The deaths include 50 in the opposition stronghold of Homs, which has been pummeled by government forces for more than three weeks. Of those, 26 died in "another massacre" in the city's Baba Amr neighborhood, the LCC said. Thirty-five others died in the suburbs of Hama, where hundreds were also injured in a fifth day of shelling.
Another opposition group, the Syrian Observatory for Human Rights, said five members of the Syrian army were killed in predawn clashes with defected soldiers in Daraa province.
The deaths followed a grim day Monday, when 144 people died nationwide, the LCC said.
CNN and other media outlets cannot independently verify opposition or government reports because Syria has severely limited access to the country by foreign journalists. But the vast majority of reports from the ground indicate that government forces are killing citizens in an attempt to wipe out civilians seeking al-Assad's ouster.
Al-Assad's regime has "subjected residents in several cities to indiscriminate bombardment by tank and rocket fire," Pascoe, the U.N.'s undersecretary general for political affairs, told the Security Council. In addition to the rising numbers of dead and wounded, about 25,000 people have registered as refugees in neighboring countries and 100,000 to 200,000 are displaced within Syria, he said.
Clinton, asked at a Senate Appropriations Committee whether al-Assad should be viewed as a war criminal, said, "I think that based on definitions of war criminal and crimes against humanity, there would be an argument to be made that he would fit into that category."
Asked about making that argument before the world community, Clinton said, "I think people have been putting forth the argument, but I also think from long experience that could complicate a resolution of a difficult, complex situation because it limits options to persuade leaders perhaps to step down from power."
Clinton's comments echoed remarks last week by Tunisian President Moncef Marzouki, who told an international "Friends of Syria" conference last week that "closing all exits" for al-Assad and his lieutenants would likely trigger more bloodshed. Tuesday, Marzouki spokesman Anden Mansar said the country has offered al-Assad political asylum in hopes of bringing about an end to the violence.
"If the Syrian president's departure to another country, including Tunisia, helps bring about a settlement to the political crisis in Syria, Tunisia will be ready to lend its assistance," added Mr. Mansar in a communique carried by the state news agency TAP.
Marzouki took office 11 months after the January 2011 revolt that toppled longtime Tunisian strongman Zine el Abidine Ben Ali and kicked off the regional upheaval now known as the "Arab Spring." Syrian opposition activists began demonstrating against al-Assad two months later, leading to the bloodshed that now wracks the country.
Earlier Tuesday, Syrian Foreign Minister Walid Moallem insisted that no regime cares more about its citizens than that of Syria.
"We are not happy to see brothers killing each other," he said. No one in Syria is dying from hunger or illness, he said, and the government is providing all necessary services despite an "economic international boycott."
The LCC said about 9,000 people have been killed since the government launched its crackdown on dissidents in March. The Syrian government says that more than 2,000 members of its security forces have been killed by "terrorists" during that same period.
International pressure on Damascus continued to mount Tuesday as the U.N. Human Rights Council met in Geneva, Switzerland, to hear more on an International Commission of Inquiry report saying Syrian government officials were responsible for "crimes against humanity" committed by security forces against opposition members.
U.N. Human Rights Commissioner Navi Pillay told the council her office has received "disturbing reports of a rapidly deteriorating human rights and humanitarian situation. Recent reports further indicate that Syrian military and security forces have launched massive campaigns of arrest, arbitrarily detaining thousands of protesters, as well as activists and others suspected of anti-government activities."
The cities of Hama and Homs have borne the brunt of the violence, she said. During government blockades, residents cannot obtain food, water or medical supplies and some cannot reach hospitals, she said. The hospitals themselves are overwhelmed, with citizens setting up makeshift clinics lacking medical supplies.
Some reports suggest more than 500 children have been killed since the unrest began in March, Pillay said. The Syrian government reported 2,493 civilians and 1,345 soldiers and police killed between March and January 18 of this year, she said, but "according to information available to my office, the actual numbers may far exceed these figures."
The Syrian government has been somewhat cooperative, allowing Arab League observers into the country as well as giving controlled access to aid groups, she said. The Arab League later suspended its monitoring mission amid ongoing violence.
"However, these steps pale into insignificance in the face of the continuing onslaught of violence and arrest against people by state actors," Pillay said. "In light of this and in the face of the unspeakable violations that take place every moment, I remain convinced that referring the situation of Syria to the International Criminal Court will be a step in the right direction."
Syria's parliament representative to the council, Fayssal Al-Hamwi, denounced the session and eventually walked out of the meeting, according to the state-run Syrian Arab News Agency.
Al-Hamwi said the "true goal" of the session is to cover up "violence and murder committed by armed terrorist groups against innocent civilians," SANA reported.
Unilateral economic sanctions against Syria, he said, "are the ugliest violations of human rights, because they target foremost civilian populations including children, women and the elderly."
"The delegation of the Syrian Arab Republic announces non-acknowledgement of the legitimacy of this session,'' he said, according to SANA.
On Monday, the European Union slapped new sanctions on the Syrian government. The EU will freeze the assets of several ministers in the al-Assad regime, and will freeze Syrian Central Bank assets in the EU.
The moves "will put further pressure on those who are responsible for the ruthless campaign of repression in Syria," Catherine Ashton, the EU foreign policy chief, said in a written statement. "The measures target the regime and its ability to conduct the appalling violence against civilians. As long as the repression continues, the EU will keep imposing sanctions."
The International Commission of Inquiry said in its report that U.N. bodies probing the crimes should identify perpetrators and hold them accountable. It said it had turned over a list of those believed to be responsible to Pillay's office.
Meanwhile, British photographer Paul Conroy, who was wounded in an attack that left two other journalists dead last week in the Baba Amr neighborhood of Homs, was safe in Lebanon Tuesday after being smuggled out of Syria, the international activist network Avaaz said.
London's Sunday Times confirmed Conroy was in Lebanon. But Avaaz said that of the roughly 50 people who tried to escape Homs with him, 23 were killed in an ambush.
Ricken Patel, the group's executive director, said journalists are "witnesses to a gigantic crime" who have to be protected. But the ambush the group faced on their way to Lebanon indicates that a key lifeline into the city has been cut off.
CNN's Joe Vaccarello, Holly Yan, Salma Abdelaziz, Kamal Ghattas and Per Nyberg contributed to this report.