With hopes of changing Moscow's stance on Damascus, U.S. Secretary of State Hillary Clinton said that Russia's relationship with President Bashar al-Assad's regime is going to make the violence in Syria worse.

[The Russians] are telling me they don't want to see a civil war. I have been telling them their policy is going to help to contribute to a civil war, Clinton said during a visit to Denmark on Thursday.

In the past week, Russia has guardedly softened its stance on Syria. It joined the rest of the United Nations Security Council in condemning last Friday's massacre in Houla and Foreign Minister Sergei Lavrov said on Wednesday that ending the violence in Syria is more important than keeping Assad in power, according to RIA Novosti.

However, Moscow still believes that the 108 civilians in Houla -- almost half of them children under 10 years old -- were killed by the opposition, not Assad's forces, a politically important stance since a new shipment of Russian arms is allegedly arriving at a Syrian port as soon as Friday.

We have to bring the Russians on board because the dangers we face are terrible, Clinton said during a visit to Denmark on Thursday.

Meanwhile, Arab leaders are trying to pressure Syria's other ally in the Security Council -- China. Tunisian President Moncef Marzouki, who came to power after his country's Arab Spring protests, said on Thursday that China should upgrade its diplomatic efforts in order to stop further bloodshed, Reuters reported.  

China could play a decisive role in halting the suffering of the Syrian people and closing off the option of military intervention, by pushing for a scenario similar to the one in Yemen, Marzouki said in a speech at a Arab-China cooperation forum in Tunisia, referring to the negotiation that led to President Ali Abdullah Saleh's resignation in February. Russia has been in favor of a Yemen-style approach to Syria and tried, so far unsuccessfully, to broker talks between the government and the opposition.

We hope (China) will redouble its effort to stop the machine of violence and death and to put more pressure on the Syrian government to respect its commitments under the Annan plan, Kuwaiti Foreign Minister Sheikh Sabah Khaled al-Sabah stated at the summit.

Together, China and Russia have vetoed two Security Council resolutions condemning Assad and indicated that they would block a third, which has hampered the United Nations' effectiveness in dealing with the Syrian uprising. Both countries are against military intervention in Syria, although both also reluctantly accepted Annan's peace plan and approved sending a small team of U.N. observers to Damascus.

Clinton said on Thursday that without a strong U.N. mandate, the violence in Syria could morph into a civil war in a country that would be riven by sectarian divides, which then could morph into a proxy war in the region if Iran, another friend of Assad, decides to increase its military presence in Syria.